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Journal articles on the topic 'Differential Algebraic Inequality'

Author: Grafiati

Published: 6 September 2023

Last updated: 31 July 2025

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1

Reis, Timo, and Matthias Voigt. "The Dissipation Inequality for Differential-Algebraic Systems." PAMM 14, no. 1 (2014): 11–14. http://dx.doi.org/10.1002/pamm.201410004.

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2

Reis, Timo, Olaf Rendel, and Matthias Voigt. "The Kalman–Yakubovich–Popov inequality for differential-algebraic systems." Linear Algebra and its Applications 485 (November 2015): 153–93. http://dx.doi.org/10.1016/j.laa.2015.06.021.

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3

Allouche, Benyamine, Antoine Dequidt, Laurent Vermeiren, and Michel Dambrine. "Modeling and PDC fuzzy control of planar parallel robot." International Journal of Advanced Robotic Systems 14, no. 1 (2017): 172988141668711. http://dx.doi.org/10.1177/1729881416687112.

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Many works in the literature have studied the kinematical and dynamical issues of parallel robots. But it is still difficult to extend the vast control strategies to parallel mechanisms due to the complexity of the model-based control. This complexity is mainly caused by the presence of multiple closed kinematic chains, making the system naturally described by a set of differential–algebraic equations. The aim of this work is to control a two-degree-of-freedom parallel manipulator. A mechanical model based on differential–algebraic equations is given. The goal is to use the structural characte

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Uppal, Tarun, Soumyendu Raha, and Suresh Srivastava. "Inverse Simulation for Gas Turbine Engine Control through Differential Algebraic Inequality Formulation." International Journal of Turbo & Jet-Engines 35, no. 4 (2018): 373–83. http://dx.doi.org/10.1515/tjj-2016-0057.

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Abstract Modern day gas turbines are prime movers in land, air and sea. They have stringent performance requirements to meet the complex mission objectives. Optimal control strategies can help them meet their performance objectives more efficiently. A novel inverse simulation method for optimal control and system analysis studies using Differential Algebraic Equality/Inequality (DAE/DAI) technique is brought out in this paper with a case study. The gas turbine model together with safety constraints and performance specifications is represented as a high index DAI/DAE system. The solution for t

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Evangelos, Fountas, and Milioris Konstantinos. "Marshallian and Hicksian demand functions without calculus." Journal of Information and Optimization Sciences 46, no. 3 (2025): 579–90. https://doi.org/10.47974/jios-1316.

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This study introduces an innovative method for deriving the Marshallian and Hicksian demand functions without the need of calculus, thus enhancing the accessibility of these fundamental economic models for audiences with less mathematical expertise. Conventional derivations of these demand functions employ calculus to optimize utility and expenditure within restrictions, potentially restricting accessibility in educational contexts and practical implementations. We utilize algebraic methods, such as Cauchy’s inequality and the Arithmetic Mean-Geometric Mean [1], [3] (AM-GM) inequality, to deri

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Qingfei, Pan, Zhang Zifang, and Huang Jingchang. "Stability of the Stochastic Reaction-Diffusion Neural Network with Time-Varying Delays andp-Laplacian." Journal of Applied Mathematics 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/405939.

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The main aim of this paper is to discuss moment exponential stability for a stochastic reaction-diffusion neural network with time-varying delays andp-Laplacian. Using the Itô formula, a delay differential inequality and the characteristics of the neural network, the algebraic conditions for the moment exponential stability of the nonconstant equilibrium solution are derived. An example is also given for illustration.

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7

Pop, Nicolae. "Generalized Newton’s method for solving nonlinear and nondifferentiable algebraic systems." Journal of Numerical Analysis and Approximation Theory 44, no. 1 (2015): 93–99. http://dx.doi.org/10.33993/jnaat441-1058.

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In this paper a model based on non-smooth equations is proposed for solving a non-linear and non-differential equation obtained by discretization of a quasi-variational inequality that models the frictional contact problem. The main aim of this paper is to show that the Newton method based on the plenary hull of the Clarke generalized Jacobians (the non-smooth damped Newton method) can be implemented for solving Lipschitz non-smooth equation.

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8

Lê, Công-Trình, and Tien-Son Phạm. "On tangent cones at infinity of algebraic varieties." Journal of Algebra and Its Applications 17, no. 08 (2018): 1850143. http://dx.doi.org/10.1142/s0219498818501438.

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In this paper, we define the geometric and algebraic tangent cones at infinity of algebraic varieties and establish the following version at infinity of Whitney’s theorem [Local properties of analytic varieties, in Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse) (Princeton University Press, Princeton, N. J., 1965), pp. 205–244; Tangents to an analytic variety, Ann. of Math. 81 (1965) 496–549]: The geometric and algebraic tangent cones at infinity of complex algebraic varieties coincide. The proof of this fact is based on a geometric characterization of the geome

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9

Reis, Timo, and Matthias Voigt. "The Kalman–Yakubovich–Popov inequality for differential-algebraic systems: Existence of nonpositive solutions." Systems & Control Letters 86 (December 2015): 1–8. http://dx.doi.org/10.1016/j.sysconle.2015.09.003.

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10

Wu, Dongli, Hao Zhang, Yunping Liu, Weihua Fang, and Yan Wang. "Real-Time Trajectory Planning and Control for Constrained UAV Based on Differential Flatness." International Journal of Aerospace Engineering 2022 (June 20, 2022): 1–17. http://dx.doi.org/10.1155/2022/8004478.

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The trajectory planning of UAV with nonholonomic constraints is usually taken as differential algebraic equation to solve the optimal control problem of functional extremum under the condition of inequality constraints. However, it can be challenging to meet the requirements of real-time for the high complexity. A differential flat theory based on B-spline trajectory planning can replace the optimal control problem with nonlinear programming and be a good means to achieve the efficient trajectory planning of an UAV under multiple dynamic constraints. This research verifies the feasibility of t

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11

Wu, Qiong, Zhimin Yao, Zhouping Yin, and Hai Zhang. "Fin-TS and Fix-TS on fractional quaternion delayed neural networks with uncertainty via establishing a new Caputo derivative inequality approach." Mathematical Biosciences and Engineering 19, no. 9 (2022): 9220–43. http://dx.doi.org/10.3934/mbe.2022428.

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<abstract><p>This paper investigates the finite time synchronization (Fin-TS) and fixed time synchronization (Fix-TS) issues on Caputo quaternion delayed neural networks (QDNNs) with uncertainty. A new Caputo fractional differential inequality is constructed, then Fix-TS settling time of the positive definite function is estimated, which is very convenient to derive Fix-TS condition to Caputo QDNNs. By designing the appropriate self feedback and adaptive controllers, the algebraic discriminant conditions to achieve Fin-TS and Fix-TS on Caputo QDNNs are proposed based on quaternion

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12

Siddiqui, Aliya Naaz, Ali Hussain Alkhaldi, and Lamia Saeed Alqahtani. "Generalized Wintgen Inequality for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature." Mathematics 10, no. 10 (2022): 1727. http://dx.doi.org/10.3390/math10101727.

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The geometry of Hessian manifolds is a fruitful branch of physics, statistics, Kaehlerian and affine differential geometry. The study of inequalities for statistical submanifolds in Hessian manifolds of constant Hessian curvature was truly initiated in 2018 by Mihai, A. and Mihai, I. who dealt with Chen-Ricci and Euler inequalities. Later on, Siddiqui, A.N., Ahmad K. and Ozel C. came with the study of Casorati inequality for statistical submanifolds in the same ambient space by using algebraic technique. Also, Chen, B.-Y., Mihai, A. and Mihai, I. obtained a Chen first inequality for such subma

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13

Li, Xiaofan, Yuan Ge, Hongjian Liu, Huiyuan Li, and Jian-an Fang. "New Results on Synchronization of Fractional-Order Memristor‐Based Neural Networks via State Feedback Control." Complexity 2020 (September 9, 2020): 1–11. http://dx.doi.org/10.1155/2020/2470972.

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This paper addresses the synchronization issue for the drive-response fractional-order memristor‐based neural networks (FOMNNs) via state feedback control. To achieve the synchronization for considered drive-response FOMNNs, two feedback controllers are introduced. Then, by adopting nonsmooth analysis, fractional Lyapunov’s direct method, Young inequality, and fractional-order differential inclusions, several algebraic sufficient criteria are obtained for guaranteeing the synchronization of the drive-response FOMNNs. Lastly, for illustrating the effectiveness of the obtained theoretical result

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14

Zhao, Shuyue, Kelin Li, and Weiyi Hu. "Synchronization in Finite Time of Fuzzy Neural Networks with Hybrid Delays and Uncertain Nonlinear Perturbations." Advances in Fuzzy Systems 2022 (July 5, 2022): 1–22. http://dx.doi.org/10.1155/2022/1448819.

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This paper deals with the finite-time synchronization problem of a class of fuzzy neural networks with hybrid delays and uncertain nonlinear perturbations. By applying the famous finite-time stability theory, combining differential inequality techniques, and the analysis approach, several new algebraic sufficient criteria are obtained to realize finite-time synchronization between the drive system and the response system by designing a state feedback controller and an adaptive controller. Taking discrete delays, distributed delays, and uncertain nonlinear perturbations into account in fuzzy ce

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15

Yuldashev, T. K., and E. T. Karimov. "Mixed type integro-differential equation with fractional order Caputo operators and spectral parameters." Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta 57 (May 2021): 190–205. http://dx.doi.org/10.35634/2226-3594-2021-57-10.

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The issues of unique solvability of a boundary value problem for a mixed type integro-differential equation with two Caputo time-fractional operators and spectral parameters are considered. A mixed type integro-differential equation is a partial integro-differential equation of fractional order in both positive and negative parts of multidimensional rectangular domain under consideration. The fractional Caputo operator's order is less in the positive part of the domain, than the order of Caputo operator in the negative part of the domain. Using the method of Fourier series, two systems of coun

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16

Reis, Timo, and Matthias Voigt. "Reprint of “The Kalman–Yakubovich–Popov inequality for differential-algebraic systems: Existence of nonpositive solutions”." Systems & Control Letters 95 (September 2016): 3–10. http://dx.doi.org/10.1016/j.sysconle.2016.05.010.

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17

Bennett, Jonathan, and Neal Bez. "Generating monotone quantities for the heat equation." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 756 (2019): 37–63. http://dx.doi.org/10.1515/crelle-2017-0025.

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AbstractThe purpose of this article is to expose and further develop a simple yet surprisingly far-reaching framework for generating monotone quantities for positive solutions to linear heat equations in euclidean space. This framework is intimately connected to the existence of a rich variety of algebraic closure properties of families of sub/super-solutions, and more generally solutions of systems of differential inequalities capturing log-convexity properties such as the Li–Yau gradient estimate. Various applications are discussed, including connections with the general Brascamp–Lieb inequa

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18

Yu, Tianhu, Shengqiang Liu, Huamin Wang, Yingjia Cui, and Dengqing Cao. "Robust delay-dependent stability of uncertain inertial neural networks with impulsive effects and distributed-delay." International Journal of Biomathematics 12, no. 01 (2019): 1950010. http://dx.doi.org/10.1142/s1793524519500104.

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The robust stability problem of uncertain inertial neural networks with impulsive effects and distributed-delay is considered in the present paper. The average impulsive interval and differential inequality for delay differential equations are used to obtain the global exponential stability of the inertial neural networks. The robust distributed-delay-dependent stability criteria here are proposed in terms of both linear matrix inequalities and algebraic inequalities. Our results can not only be used to obtain the stability of the uncertain inertial neural network with impulsive disturbance, b

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19

Giorgi, Claudio, and Angelo Morro. "Strain-Rate and Stress-Rate Models of Nonlinear Viscoelastic Materials." Mathematics 12, no. 19 (2024): 3011. http://dx.doi.org/10.3390/math12193011.

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The paper is devoted to the modeling of nonlinear viscoelastic materials. The constitutive equations are considered in differential form via relations between strain, stress, and their derivatives in the Lagrangian description. The thermodynamic consistency is established by using the Clausius–Duhem inequality through a procedure that involves two uncommon features. Firstly, the entropy production is regarded as a positive-valued constitutive function per se. This view implies that the inequality is in fact an equation. Secondly, this statement of the second law is investigated by using an alg

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20

Luo, Fei, Weiyi Hu, Enli Wu, and Xiufang Yuan. "Global Exponential Stability of Impulsive Delayed Neural Networks with Parameter Uncertainties and Reaction–Diffusion Terms." Mathematics 12, no. 15 (2024): 2395. http://dx.doi.org/10.3390/math12152395.

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In this paper, we present a method to achieve exponential stability in a class of impulsive delayed neural networks containing parameter uncertainties, time-varying delays, and impulsive effect and reaction–diffusion terms. By using an integro-differential inequality with impulsive initial conditions and employing the M-matrix theory and the nonlinear measure approach, some new sufficient conditions ensuring the global exponential stability and global robust exponential stability of the considered system are derived. In particular, the results obtained are presented by simple algebraic inequal

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21

Fan, Yingjie, Zhongliang Wei, and Meixuan Li. "Switching-Jumps-Dependent Quasi-Synchronization Criteria for Fractional-Order Memrisive Neural Networks." Fractal and Fractional 7, no. 1 (2022): 12. http://dx.doi.org/10.3390/fractalfract7010012.

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This paper investigates the switching-jumps-dependent quasi-synchronization issue for fractional-order memristive neural networks (FMNNs). First, a simplied linear feedback controller is applied. Then, in terms of several fractional order differential inequalities and two kinds of Lyapunov functions, two quasi-synchronization criteria expressed by linear matrix inequality (LMI)-based form and algebraic form are established, respectively. Meanwhile, the co-designed scheme for error bound and control gain is established. Compared with the previous quasi-synchronization results, a strong assumpti

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22

Rossovskii, L. E., and A. A. Tovsultanov. "The Dirichlet Problem for an Elliptic Functional Differential Equation with the Compressed, Expanded, and Rotated Argument." Lobachevskii Journal of Mathematics 45, no. 4 (2024): 1495–510. http://dx.doi.org/10.1134/s1995080224601255.

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Abstract The paper is devoted to the Dirichlet problem in a plain bounded domain for a linear divergent-form second-order functional differential equation with the compressed (expanded) and rotated argument of the highest derivatives of the unknown function. Necessary and sufficient conditions for the Gårding-type inequality are obtained in algebraic form. The result may depend not only on the absolute value of the coefficients but also on their signature. Under some restrictions on the structure of the operator and the geometry of the domain, the questions of existence, uniqueness, and smooth

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23

Bouassem, Karim, Abdellatif El Assoudi, Jalal Soulami, and El Hassane El Yaagoubi. "Unknown Input Observer Design for a Class of Linear Descriptor Systems." E3S Web of Conferences 229 (2021): 01019. http://dx.doi.org/10.1051/e3sconf/202122901019.

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This paper addresses the problem of unknown inputs observer (UIO) design for a class of linear descriptor systems. The unknown inputs affect both state and output of the system. The basic idea of the proposed approach is based on the separation between dynamic and static relations in the descriptor model. Firstly, the method used to separate the differential part from the algebraic part is developed. Secondly, an observer design permitting the simultaneous estimation of the system state and the unknown inputs is proposed. The developed approach for the observer design is based on the synthesis

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24

KOJIC, Vedran. "On a Geometric Programming Approach to Profit Maximization: The Case of CES Technology." Eurasia Proceedings of Science Technology Engineering and Mathematics 18 (October 20, 2022): 7–15. http://dx.doi.org/10.55549/epstem.1182630.

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The profit maximization problem takes a central place in the theory of the firm, especially when conditions for perfect competition hold. In this paper, we solve the profit maximization problem of a perfectly competitive firm when the constant elasticity of substitution (CES) production function with n≥2 inputs describes its technology. Commonly, this problem is solved by using multivariable differential calculus. However, to avoid tedious algebraic manipulations and bypass checking nontrivial necessary and sufficient conditions, we employ geometric programming (GP), and the power mean inequal

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25

Hu, Weiyi, Kelin Li, and Shuyue Zhao. "Periodicity of Nonautonomous Fuzzy Neural Networks with Reaction-Diffusion terms and Distributed Time Delays." Mathematical Problems in Engineering 2022 (October 13, 2022): 1–15. http://dx.doi.org/10.1155/2022/9186393.

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In this paper, the periodicity of a class of nonautonomous fuzzy neural networks with impulses, reaction-diffusion terms, and distributed time delays are investigated. By establishing an integro-differential inequality with impulsive initial conditions and time-varying coefficients, employing the M -matrix theory, Poincar mappings, and fixed point theory, several new sufficient conditions to ensure the periodicity and global exponential stability of the formulated system are obtained. It is worthwhile to mention that our technical methods are practical, in the sense that all new stability cond

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26

Yuldashev, Tursun K., and Erkinjon T. Karimov. "Inverse Problem for a Mixed Type Integro-Differential Equation with Fractional Order Caputo Operators and Spectral Parameters." Axioms 9, no. 4 (2020): 121. http://dx.doi.org/10.3390/axioms9040121.

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The questions of the one-value solvability of an inverse boundary value problem for a mixed type integro-differential equation with Caputo operators of different fractional orders and spectral parameters are considered. The mixed type integro-differential equation with respect to the main unknown function is an inhomogeneous partial integro-differential equation of fractional order in both positive and negative parts of the multidimensional rectangular domain under consideration. This mixed type of equation, with respect to redefinition functions, is a nonlinear Fredholm type integral equation

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27

Chieh-Chuan, Feng. "Control Systems in the Presence of Actuators or Sensors Degradation." International Journal of Trend in Scientific Research and Development 1, no. 5 (2017): 97–104. https://doi.org/10.31142/ijtsrd2250.

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In this paper, we design controller that combines an observer and a control to handle systems subject to actuator or sensor degradation including complete failure . The observer contains a pre filter, an adaptive law, and a modified Luenberger observer that achieves estimation of system state and estimation of conditions of actuator or sensor. We have shown that if a set of differential Riccati inequatities DRI is satisfied then the system can be stabilized under actuator degrad ation. While in sensor degradation case if an Algebraci Riccati inequality ARI and a DRI are satisfied then the syst

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28

Uppal, T., S. Raha, and S. Srivastava. "Trajectory feasibility evaluation using path prescribed control of unmanned aerial vehicle in differential algebraic equations framework." Aeronautical Journal 121, no. 1240 (2017): 770–89. http://dx.doi.org/10.1017/aer.2017.36.

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ABSTRACTMission simulation is a critical activity in the development and operation of Unmanned Aerial Vehicles (UAVs). It is important to ascertain the feasibility of a trajectory in a mission. In this work, an algorithm has been developed for feasibility study of a trajectory of a UAV using prescribed path optimal control through an inverse simulation method. This has been done under a Differential Algebraic Equations (DAE)/Inequalities (DAI) framework. The UAV model together with constraints is represented as a high index DAE system. The trajectory that UAV shall take is prescribed as one of

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29

Tamba, Tua A., Jonathan Chandra, and Bin Hu. "Stability analysis of a hybrid DC-DC buck converter model using dissipation inequality and convex optimization." Journal of Mechatronics, Electrical Power, and Vehicular Technology 14, no. 1 (2023): 47–54. http://dx.doi.org/10.14203/j.mev.2023.v14.47-54.

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The stability analysis of a DC-DC buck converter is a challenging problem due to the hybrid systems characteristic of its dynamics. Such a challenge arises from the buck converter operation which depends upon the ON/OFF logical transitions of its electronic switch component to correspondingly activate different continuous vector fields of the converter’s temporal dynamics. This paper presents a sum of squares (SOS) polynomial optimization approach for stability analysis of a hybrid model of buck converter which explicitly takes into account the converter’s electronic switching behavior. The pr

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30

Pan, Jie, and Lianglin Xiong. "Novel Criteria of Stability for Delayed Memristive Quaternionic Neural Networks: Directly Quaternionic Method." Mathematics 9, no. 11 (2021): 1291. http://dx.doi.org/10.3390/math9111291.

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In this paper, we fixate on the stability of varying-time delayed memristive quaternionic neural networks (MQNNs). With the help of the closure of the convex hull of a set the theory of differential inclusion, MQNN are transformed into variable coefficient continuous quaternionic neural networks (QNNs). The existence and uniqueness of the equilibrium solution (ES) for MQNN are concluded by exploiting the fixed-point theorem. Then a derivative formula of the quaternionic function’s norm is received. By utilizing the formula, the M-matrix theory, and the inequality techniques, some algebraic sta

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31

Shao, Xing-Guo, Zhen-Cai Zhu, Qing-Guo Wang, Peter CY Chen, Bin Zi, and Guo-Hua Cao. "Non-smooth dynamical analysis and experimental validation of the cable-suspended parallel manipulator." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 226, no. 10 (2012): 2456–66. http://dx.doi.org/10.1177/0954406211435585.

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The cable-suspended parallel manipulator replaces the rigid links of traditional parallel robot. The unilateral property of the cable complicates the dynamic analysis of such manipulator and further induces difficulty in control problem. The set-valued tension law is proposed to model the unilateral constraint of the cable, and the dynamics of cable-suspended parallel manipulator is analyzed in the framework of non-smooth dynamics. The resulting non-smooth dynamics model consists of a set of differential–algebraic equations with inequality constraints. Its solution is found by the Moreau midpo

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32

Ouarid, Kaoutar, Abdellatif El Assoudi, Jalal Soulami, and El Hassane El Yaagoubi. "Observer Design for Simultaneous State and Fault Estimation for a Class of Discrete-time Descriptor Linear Models." E3S Web of Conferences 229 (2021): 01020. http://dx.doi.org/10.1051/e3sconf/202122901020.

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This paper investigates the problem of observer design for simultaneous states and faults estimation for a class of discrete-time descriptor linear models in presence of actuator and sensor faults. The idea of the present result is based on the second equivalent form of implicit model [1] which permits to separate the differential and algebraic equations in the considered singular model, and the use of an explicit augmented model structure. At that stage, an observer is built to estimate simultaneously the unknown states, the actuator faults, and the sensor faults. Next, the explicit structure

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33

Wohlmuth, Barbara. "Variationally consistent discretization schemes and numerical algorithms for contact problems." Acta Numerica 20 (April 28, 2011): 569–734. http://dx.doi.org/10.1017/s0962492911000079.

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We consider variationally consistent discretization schemes for mechanical contact problems. Most of the results can also be applied to other variational inequalities, such as those for phase transition problems in porous media, for plasticity or for option pricing applications from finance. The starting point is to weakly incorporate the constraint into the setting and to reformulate the inequality in the displacement in terms of a saddle-point problem. Here, the Lagrange multiplier represents the surface forces, and the constraints are restricted to the boundary of the simulation domain. Hav

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34

Aldawish, Ibtisam, Mohamed Jleli, and Bessem Samet. "On Hermite–Hadamard-Type Inequalities for Functions Satisfying Second-Order Differential Inequalities." Axioms 12, no. 5 (2023): 443. http://dx.doi.org/10.3390/axioms12050443.

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Hermite–Hadamard inequality is a double inequality that provides an upper and lower bounds of the mean (integral) of a convex function over a certain interval. Moreover, the convexity of a function can be characterized by each of the two sides of this inequality. On the other hand, it is well known that a twice differentiable function is convex, if and only if it admits a nonnegative second-order derivative. In this paper, we obtain a characterization of a class of twice differentiable functions (including the class of convex functions) satisfying second-order differential inequalities. Some s

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35

Tariq, Muhammad, Soubhagya Kumar Sahoo, Sotiris K. Ntouyas, Omar Mutab Alsalami, Asif Ali Shaikh, and Kamsing Nonlaopon. "Some New Refinements of Trapezium-Type Integral Inequalities in Connection with Generalized Fractional Integrals." Axioms 11, no. 10 (2022): 508. http://dx.doi.org/10.3390/axioms11100508.

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The main objective of this article is to introduce a new notion of convexity, i.e., modified exponential type convex function, and establish related fractional inequalities. To strengthen the argument of the paper, we introduce two new lemmas as auxiliary results and discuss some algebraic properties of the proposed notion. Considering a generalized fractional integral operator and differentiable mappings, whose initial absolute derivative at a given power is a modified exponential type convex, various improvements of the Hermite–Hadamard inequality are presented. Thanks to the main results, s

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36

Srivastava, Hari Mohan, Muhammad Tariq, Pshtiwan Othman Mohammed, Hleil Alrweili, Eman Al-Sarairah, and Manuel De La De La Sen. "On Modified Integral Inequalities for a Generalized Class of Convexity and Applications." Axioms 12, no. 2 (2023): 162. http://dx.doi.org/10.3390/axioms12020162.

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In this paper, we concentrate on and investigate the idea of a novel family of modified p-convex functions. We elaborate on some of this newly proposed idea’s attractive algebraic characteristics to support it. This is used to study some novel integral inequalities in the frame of the Hermite–Hadamard type. A unique equality is established for differentiable mappings. The Hermite–Hadamard inequality is extended and estimated in a number of new ways with the help of this equality to strengthen the findings. Finally, we investigate and explore some applications for some special functions. We thi

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Bai, Zhenyu, and Chuanzhi Bai. "The Existence and Averaging Principle for Caputo Fractional Stochastic Delay Differential Systems with Poisson Jumps." Axioms 13, no. 1 (2024): 68. http://dx.doi.org/10.3390/axioms13010068.

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In this paper, we obtain the existence and uniqueness theorem for solutions of Caputo-type fractional stochastic delay differential systems(FSDDSs) with Poisson jumps by utilizing the delayed perturbation of the Mittag–Leffler function. Moreover, by using the Burkholder–Davis–Gundy inequality, Doob’s martingale inequality, and Hölder inequality, we prove that the solution of the averaged FSDDSs converges to that of the standard FSDDSs in the sense of Lp. Some known results in the literature are extended.

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38

MASON, GEOFFREY. "VECTOR-VALUED MODULAR FORMS AND LINEAR DIFFERENTIAL OPERATORS." International Journal of Number Theory 03, no. 03 (2007): 377–90. http://dx.doi.org/10.1142/s1793042107000973.

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We consider holomorphic vector-valued modular forms F of integral weight k on the full modular group Γ = SL(2, ℤ) corresponding to representations of Γ of arbitrary finite dimension p. Assuming that the component functions of F are linearly independent, we prove that the inequality k ≥ 1 - p always holds, and that equality holds only in the trivial case when p = 1 and k = 0. For any p ≥ 2, we show how to construct large numbers of representations of Γ for which k = 2 - p. The key idea is to consider representations of Γ on spaces of solutions of certain linear differential equations whose coef

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Alshabanat, Amal, Eman Almoalim, Mohamed Jleli, and Bessem Samet. "A Time-Fractional Differential Inequality of Sobolev Type on an Annulus." Axioms 12, no. 10 (2023): 993. http://dx.doi.org/10.3390/axioms12100993.

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Several phenomena from natural sciences can be described by partial differential equations of Sobolev-type. On the other hand, it was shown that in many cases, the use of fractional derivatives provides a more realistic model than the use of standard derivatives. The goal of this paper is to study the nonexistence of weak solutions to a time-fractional differential inequality of Sobolev-type. Namely, we give sufficient conditions for the nonexistence or equivalently necessary conditions for the existence. Our method makes use of the nonlinear capacity method, which consists in making an approp

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Zhu, Xinyue, Wei Li, and Xueping Luo. "Stability for a Class of Differential Set-Valued Inverse Variational Inequalities in Finite Dimensional Spaces." Axioms 11, no. 9 (2022): 475. http://dx.doi.org/10.3390/axioms11090475.

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In this paper, we introduce and study a new class of differential set-valued inverse variational inequalities in finite dimensional spaces. By applying a result on differential inclusions involving an upper semicontinuous set-valued mapping with closed convex values, we first prove the existence of Carathéodory weak solutions for differential set-valued inverse variational inequalities. Then, by the existence result, we establish the stability for the differential set-valued inverse variational inequality problem when the constraint set and the mapping are perturbed by two different parameters

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41

Raffoul, Youssef N. "Boundedness and stability in nonlinear systems of differential equations using a modified variation of parameters formula." Cubo (Temuco) 25, no. 1 (2023): 37–55. http://dx.doi.org/10.56754/0719-0646.2501.037.

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In this research we introduce a new variation of parameters for systems of linear and nonlinear ordinary differential equations. We use known mathematical methods and techniques including Gronwall’s inequality and fixed point theory to obtain boundedness on all solutions and stability results on the zero solution.

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Agarwal, Ravi P., Snezhana Hristova, and Donal O’Regan. "Boundary Value Problems for Fractional Differential Equations of Caputo Type and Ulam Type Stability: Basic Concepts and Study." Axioms 12, no. 3 (2023): 226. http://dx.doi.org/10.3390/axioms12030226.

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Boundary value problems are very applicable problems for different types of differential equations and stability of solutions, which are an important qualitative question in the theory of differential equations. There are various types of stability, one of which is the so called Ulam-type stability, and it is a special type of data dependence of solutions of differential equations. For boundary value problems, this type of stability requires some additional understanding, and, in connection with this, we discuss the Ulam-Hyers stability for different types of differential equations, such as or

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Orhan, Halit, and Luminiţa-Ioana Cotîrlă. "Fekete-Szegö Inequalities for Some Certain Subclass of Analytic Functions Defined with Ruscheweyh Derivative Operator." Axioms 11, no. 10 (2022): 560. http://dx.doi.org/10.3390/axioms11100560.

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In our present investigation, we introduce and study some new subclasses of analytic functions associated with Ruscheweyh differential operator Dr. We obtain a Fekete–Szegö inequality for certain normalized analytic function defined on the open unit disk for which Drl′(z)ϑzDrl′(z)Drl(z)1−ϑ≺ez(0≤ϑ≤1) lies in a starlike region with respect to 1 and symmetric with respect to the real axis. As a special case of this result, the Fekete–Szegö inequality for a class of functions defined through Poisson distribution series is obtained.

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Bayraktar, Bahtiyar, Péter Kórus, and Juan Eduardo Nápoles Valdés. "Some New Jensen–Mercer Type Integral Inequalities via Fractional Operators." Axioms 12, no. 6 (2023): 517. http://dx.doi.org/10.3390/axioms12060517.

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In this study, we present new variants of the Hermite–Hadamard inequality via non-conformable fractional integrals. These inequalities are proven for convex functions and differentiable functions whose derivatives in absolute value are generally convex. Our main results are established using the classical Jensen–Mercer inequality and its variants for (h,m)-convex modified functions proven in this paper. In addition to showing that our results support previously known results from the literature, we provide examples of their application.

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Agarwal, Ravi P., and Snezhana Hristova. "Ulam-Type Stability for a Boundary-Value Problem for Multi-Term Delay Fractional Differential Equations of Caputo Type." Axioms 11, no. 12 (2022): 742. http://dx.doi.org/10.3390/axioms11120742.

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A boundary-value problem for a couple of scalar nonlinear differential equations with a delay and several generalized proportional Caputo fractional derivatives is studied. Ulam-type stability of the given problem is investigated. Sufficient conditions for the existence of the boundary-value problem with an arbitrary parameter are obtained. In the study of Ulam-type stability, this parameter was chosen to depend on the solution of the corresponding fractional differential inequality. We provide sufficient conditions for Ulam–Hyers stability, Ulam–Hyers–Rassias stability and generalized Ulam–Hy

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Hao, Jianwei, Jinrong Wang, and Jiangfeng Han. "Solvability of Conformable Type Frictionless Contact Problem via Hemivariational Inequalities." Axioms 11, no. 6 (2022): 271. http://dx.doi.org/10.3390/axioms11060271.

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In this paper, we study a class of conformable frictionless contact problems with the surface traction driven by the conformable impulsive differential equation. The existence of a mild solution for conformable impulsive hemivariational inequality is obtained by the Rothe method, subjectivity of multivalued pseudomonotone operators and the property of the conformable derivative. Notice that we imply some new fractional viscoelastic constitutive laws.

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Zhang, Wenlin, Michal Fečkan, and Jinrong Wang. "The Existence of Weak Solutions for the Vorticity Equation Related to the Stratosphere in a Rotating Spherical Coordinate System." Axioms 11, no. 7 (2022): 347. http://dx.doi.org/10.3390/axioms11070347.

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In this paper, based on the Euler equation and mass conservation equation in spherical coordinates, the ratio of the stratospheric average width to the planetary radius and the ratio of the vertical velocity to the horizontal velocity are selected as parameters under appropriate boundary conditions. We establish the approximate system using these two small parameters. In addition, we consider the time dependence of the system and establish the governing equations describing the atmospheric flow. By introducing a flow function to code the system, a nonlinear vorticity equation describing the pl

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Vivas-Cortez, Miguel, Muhammad Uzair Awan, Sadia Talib, Artion Kashuri та Muhammad Aslam Noor. "Some New Post-Quantum Integral Inequalities Involving Twice (p, q)-Differentiable ψ-Preinvex Functions and Applications". Axioms 10, № 4 (2021): 283. http://dx.doi.org/10.3390/axioms10040283.

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The main motivation of this article is derive a new post-quantum integral identity using twice (p, q)-differentiable functions. Using the identity as an auxiliary result, we will obtain some new variants of Hermite–Hadamard’s inequality essentially via the class of ψ-preinvex functions. To support our results, we offer some applications to a special means of positive real numbers and twice (p, q)-differentiable functions that are in absolute value bounded as well.

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Ali, Rosihan M., Satwanti Devi, and A. Swaminathan. "Inclusion properties for a class of analytic functions defined by a second-order differential inequality." Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 112, no. 1 (2016): 117–33. http://dx.doi.org/10.1007/s13398-016-0368-1.

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Xu, Lili, Yalong Xue, Qifa Lin, and Chaoquan Lei. "Global Attractivity of Symbiotic Model of Commensalism in Four Populations with Michaelis–Menten Type Harvesting in the First Commensal Populations." Axioms 11, no. 7 (2022): 337. http://dx.doi.org/10.3390/axioms11070337.

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This article revisits the stability property of a symbiotic model of commensalism with Michaelis–Menten type harvesting in the first commensal populations. By constructing some suitable Lyapunov functions, we provide a thorough analysis of the dynamic behaviors of the subsystem composed of the second and third species. After that, by applying the stability results of this subsystem and combining with the differential inequality theory, sufficient conditions which ensure the global attractivity of the equilibria are obtained. The results obtained here essentially improve and generalize some kno

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