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Journal articles on the topic 'Integro-Differential'

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Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Parasidis, I. N. "EXTENSION AND DECOMPOSITION METHOD FOR DIFFERENTIAL AND INTEGRO-DIFFERENTIAL EQUATIONS." Eurasian Mathematical Journal 10, no. 3 (2019): 48–67. http://dx.doi.org/10.32523/2077-9879-2019-10-3-48-67.

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2

Guo, Li, Georg Regensburger, and Markus Rosenkranz. "On integro-differential algebras." Journal of Pure and Applied Algebra 218, no. 3 (March 2014): 456–73. http://dx.doi.org/10.1016/j.jpaa.2013.06.015.

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3

TÖRÖK, LEVENTE, and LÁSZLÓ B. KISH. "INTEGRO-DIFFERENTIAL STOCHASTIC RESONANCE." Fluctuation and Noise Letters 05, no. 01 (March 2005): L27—L42. http://dx.doi.org/10.1142/s0219477505002380.

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A new class of stochastic resonator (SRT) and Stochastic Resonance (SR) phenomena are described. The new SRT consist of a classical SRT, one or more time derivative circuits and the same number of time integrators. The incoming signal with additive noise is first time derivated, then passes through the classical SRT and finally it is time integrated. The resulting SR phenomena show a well defined SR. Moreover the signal transfer and SNR are the best at the high frequency end. A particular property of the new system is the much smoother output signal due to the time integration.

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4

Karkarashvili, G. S. "Fredholm integro-differential equation." Journal of Soviet Mathematics 66, no. 3 (September 1993): 2236–42. http://dx.doi.org/10.1007/bf01229590.

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5

Rangarajan, R., and Ananth Kumar S. R. "Homotopy-laplace Decomposition Method to Solve Nonlinear Differential-difference Equations." Journal of the Indian Mathematical Society 84, no. 3-4 (July 1, 2017): 255. http://dx.doi.org/10.18311/jims/2017/14928.

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In the recent literature, nonlinear differential equations, integro- differential equations, differential-difference equations and integro-differential-difference equations are studied. Laplace decomposition method and Homotopy analysis method are two powerful decomposition methods employed in the recent literature, nonlinear dierential equations, integro-differential equations, differential-difference equations and integro-differential-difference equations are studied. Laplace decomposition method and Homotopy analysis method are two powerful decomposition methods employed in the literature to solve above nonlinear problems. In the present paper a new method is proposed motivated by the above two methods to solve both nonlinear differential-difference equations and integro-differential-difference equations.

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6

Xu, Liguang, and András Prékopa. "L-operator integro-differential inequality for dissipativity of stochastic integro-differential equations." Mathematical Inequalities & Applications, no. 1 (2011): 123–34. http://dx.doi.org/10.7153/mia-14-10.

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7

Yuldashev, T. K., and S. K. Zarifzoda. "On a New Class of Singular Integro-differential Equations." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 101, no. 1 (March 30, 2021): 138–48. http://dx.doi.org/10.31489/2021m1/138-148.

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In this paper for a new class of model and non-model partial integro-differential equations with singularity in the kernel, we obtained integral representation of family of solutions by aid of arbitrary functions. Such type of integro-differential equations are different from Cauchy-type singular integro-differential equations. Cauchy-type singular integro-differential equations are studied by the methods of the theory of analytic functions. In the process of our research the new types of singular integro-differential operators are introduced and main property of entered operators are learned. It is shown that the solution of studied equation is equivalent to the solution of system of two equations with respect to x and y, one of which is integral equation and the other is integro-differential equation. Further, non-model integro-differential equations are studied by regularization method. This regularization method for non-model equation is based on selecting and analysis of a model part of the equation and reduced to the solution of two second kind Volterra type integral equations with weak singularity in the kernel. It is shown that the presence of a non-model part in the equation does not affect to the general structure of the solutions. From here investigation of the model equations for given class of the integro-differential equations becomes important. In the cases, when the solution of given integro-differential equation depends on any arbitrary functions, a Cauchy type problems are investigated.

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8

GIL', M. I. "POSITIVITY OF GREEN'S FUNCTIONS TO VOLTERRA INTEGRAL AND HIGHER ORDER INTEGRO-DIFFERENTIAL EQUATIONS." Analysis and Applications 07, no. 04 (October 2009): 405–18. http://dx.doi.org/10.1142/s0219530509001475.

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We consider Volterra integral equations and arbitrary order integro-differential equations. We establish positivity conditions and two-sided estimates for Green's functions. These results are then applied to obtain stability and positivity conditions for equations with nonlinear causal mappings (operators) and linear integro-differential parts. Such equations include differential, difference, differential-delay, integro-differential and other traditional equations.

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9

Alfredo Lorenzi. "OPERATOR EQUATIONS OF THE FIRST KIND AND INTEGRO-DIFFERENTIAL EQUATIONS OF DEGENERATE TYPE IN BANACH SPACES AND APPLICATIONS TO INTEGRO-DIFFERENTIAL PDE’S." Eurasian Journal of Mathematical and Computer Applications 1, no. 1 (2013): 50–75. http://dx.doi.org/10.32523/2306-3172-2013-1-2-50-75.

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10

Laoprasittichok, Sorasak, Sotiris K. Ntouyas, and Jessada Tariboon. "Hybrid fractional integro-differential inclusions." Discussiones Mathematicae. Differential Inclusions, Control and Optimization 35, no. 2 (2015): 151. http://dx.doi.org/10.7151/dmdico.1174.

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11

Zawistowski, Zygmunt Jacek. "Symmetries of integro-differential equations." Reports on Mathematical Physics 48, no. 1-2 (August 2001): 269–76. http://dx.doi.org/10.1016/s0034-4877(01)80088-4.

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12

Iserles, Arieh, and Yunkang Liu. "On Pantograph Integro-Differential Equations." Journal of Integral Equations and Applications 6, no. 2 (June 1994): 213–37. http://dx.doi.org/10.1216/jiea/1181075805.

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13

Melville, John. "A Linear Integro-Differential Equation." SIAM Review 33, no. 4 (December 1991): 655–56. http://dx.doi.org/10.1137/1033142.

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14

LakshmiKantham, V., S. Leela, and M. Ama Mohan Rao. "Integral and integro-differential inequalities." Applicable Analysis 24, no. 3 (January 1987): 157–64. http://dx.doi.org/10.1080/00036818708839660.

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15

Rezapour, Shahram, Hernán R. Henríquez, Velusamy Vijayakumar, Kottakkaran Sooppy Nisar, and Anurag Shukla. "A Note on Existence of Mild Solutions for Second-Order Neutral Integro-Differential Evolution Equations with State-Dependent Delay." Fractal and Fractional 5, no. 3 (September 17, 2021): 126. http://dx.doi.org/10.3390/fractalfract5030126.

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This article is mainly devoted to the study of the existence of solutions for second-order abstract non-autonomous integro-differential evolution equations with infinite state-dependent delay. In the first part, we are concerned with second-order abstract non-autonomous integro-differential retarded functional differential equations with infinite state-dependent delay. In the second part, we extend our results to study the second-order abstract neutral integro-differential evolution equations with state-dependent delay. Our results are established using properties of the resolvent operator corresponding to the second-order abstract non-autonomous integro-differential equation and fixed point theorems. Finally, an application is presented to illustrate the theory obtained.

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16

Chetverikov, V. N. "Linear Differential Operators Invertible in the Integro-differential Sense." Mathematics and Mathematical Modeling, no. 4 (December 13, 2019): 20–33. http://dx.doi.org/10.24108/mathm.0419.0000195.

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The paper studies linear differential operators in derivatives with respect to one variable. Such operators include, in particular, operators defined on infinite prolongations of evolutionary systems of differential equations with one spatial variable. In this case, differential operators in total derivatives with respect to the spatial variable are considered. In parallel, linear differential operators with one independent variable are investigated. The known algorithms for reducing the matrix to a stepwise or diagonal form are generalized to the operator matrices of both types. These generalizations are useful at points, where the functions, into which the matrix components are divided when applying the algorithm, are nonzero.In addition, the integral operator is defined as a multi-valued operator that is the right inverse of the total derivative. Linear operators that involve both the total derivatives and the integral operator are called integro-differential. An invertible operator in the integro-differential sense is an operator for which there exists a two-sided inverse integro-differential operator. A description of scalar differential operators that are invertible in this sense is obtained. An algorithm for checking the invertibility in the integro-differential sense of a differential operator and for constructing the inverse integro-differential operator is formulated.The results of the work can be used to solve linear equations for matrix differential operators arising in the theory of evolutionary systems with one spatial variable. Such operator equations arise when describing systems that are integrable by the inverse scattering method, when calculating recursion operators, higher symmetries, conservation laws and symplectic operators, and also when solving some other problems. The proposed method for solving operator equations is based on reducing the matrices defining the operator equation to a stepwise or diagonal form and solving the resulting scalar operator equations.

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17

Yang, Chuan-Fu. "Trace Formulae for Matrix Integro-Differential Operators." Zeitschrift für Naturforschung A 67, no. 3-4 (April 1, 2012): 180–84. http://dx.doi.org/10.5560/zna.2011-0068.

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In this paper, we consider the eigenvalue problems for matrix integro-differential operators with separated boundary conditions on the finite interval and find new trace formulae for the matrix integro-differential operators

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18

Ahmed, Hamdy, Mahmoud El-Borai, Hassan El-Owaidy, and Ahmed Ghanem. "Existence Solution and Controllability of Sobolev Type Delay Nonlinear Fractional Integro-Differential System." Mathematics 7, no. 1 (January 14, 2019): 79. http://dx.doi.org/10.3390/math7010079.

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Fractional integro-differential equations arise in the mathematical modeling of various physical phenomena like heat conduction in materials with memory, diffusion processes, etc. In this manuscript, we prove the existence of mild solution for Sobolev type nonlinear impulsive delay integro-differential system with fractional order 1 < q < 2. We establish the sufficient conditions for the approximate controllability of Sobolev type nonlinear impulsive delay integro-differential system with fractional order 1 < q < 2. In addition, we prove the exact null controllability of Sobolev type nonlinear impulsive delay integro-differential system with fractional order 1 < q < 2. Finally, an example is given to illustrate the obtained results.

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19

Kang, Shin Min, Zain Iqbal, Mustafa Habib, and Waqas Nazeer. "Sumudu Decomposition Method for Solving Fuzzy Integro-Differential Equations." Axioms 8, no. 2 (June 20, 2019): 74. http://dx.doi.org/10.3390/axioms8020074.

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Different results regarding different integro-differentials are usually not properly generalized, as they often do not satisfy some of the constraints. The field of fuzzy integro-differentials is very rich these days because of their different applications and functions in different physical phenomena. Solutions of linear fuzzy Volterra integro-differential equations (FVIDEs) are more generalized and have better applications. In this report, the Sumudu decomposition method (SDM) was used to find the solution to some linear and nonlinear fuzzy integro-differential equations (FIDEs). Some examples are given to show the validity of the presented method.

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20

Abdollahramezani, Sajjad, Ata Chizari, Ali Eshaghian Dorche, Mohammad Vahid Jamali, and Jawad A. Salehi. "Dielectric metasurfaces solve differential and integro-differential equations." Optics Letters 42, no. 7 (March 17, 2017): 1197. http://dx.doi.org/10.1364/ol.42.001197.

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21

GAO, XING, LI GUO, and SHANGHUA ZHENG. "CONSTRUCTION OF FREE COMMUTATIVE INTEGRO-DIFFERENTIAL ALGEBRAS BY THE METHOD OF GRÖBNER–SHIRSHOV BASES." Journal of Algebra and Its Applications 13, no. 05 (February 25, 2014): 1350160. http://dx.doi.org/10.1142/s0219498813501600.

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In this paper, we construct free commutative integro-differential algebras by applying the method of Gröbner–Shirshov bases. We establish the Composition-Diamond Lemma for free commutative differential Rota–Baxter (DRB) algebras of order n. We also obtain a weakly monomial order on these algebras, allowing us to obtain Gröbner–Shirshov bases for free commutative integro-differential algebras on a set. We finally generalize the concept of functional monomials to free differential algebras with arbitrary weight and generating sets from which to construct a canonical linear basis for free commutative integro-differential algebras.

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22

Tarang, M. "STABILITY OF THE SPLINE COLLOCATION METHOD FOR SECOND ORDER VOLTERRA INTEGRO‐DIFFERENTIAL EQUATIONS." Mathematical Modelling and Analysis 9, no. 1 (March 31, 2004): 79–90. http://dx.doi.org/10.3846/13926292.2004.9637243.

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Numerical stability of the spline collocation method for the 2nd order Volterra integro‐differential equation is investigated and connection between this theory and corresponding theory for the 1st order Volterra integro‐differential equation is established. Results of several numerical tests are presented. Straipsnyje nagrinejamas antros eiles Volteros integro‐diferencialiniu lygčiu splainu kolokaci‐jos metodo skaitinis stabilumas ir nustatytas ryšys tarp šios teorijos ir atitinkamos pirmos eiles Volterra integro‐diferencialiniu lygčiu teorijos. Pateikti keleto skaitiniu eksperimentu rezultatai.

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23

Dzhumabaev, D. S., and S. T. Mynbayeva. "NEW GENERAL SOLUTION TO A NONLINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATION." Eurasian Mathematical Journal 10, no. 4 (2019): 24–33. http://dx.doi.org/10.32523/2077-9879-2019-10-4-24-33.

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24

ZARIFZODA, Sarvar K., and Raim N. ODINAEV. "INVESTIGATION OF SOME CLASSES OF SECOND ORDER PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS WITH A POWERLOGARITHMIC SINGULARITY IN THE KERNEL." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 67 (2020): 40–54. http://dx.doi.org/10.17223/19988621/67/4.

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For a class of second-order partial integro-differential equations with a power singularity and logarithmic singularity in the kernel, integral representations of the solution manifold in terms of arbitrary constants are obtained in the class of functions vanishing with a certain asymptotic behavior. Although the kernel of the given equation is not a Fredholm type kernel, the solution of the studied equation in a class of vanishing functions is found in an explicit form. We represent a second-order integro-differential equation as a product of two first-order integro-differential operators. For these one-dimensional integro-differential operators, in the cases when the roots of the corresponding characteristic equations are real and different, real and equal and complex and conjugate, the inverse operators are found. It is found that the presence of power singularity and logarithmic singularity in the kernel affects the number of arbitrary constants in the general solution. This number, depending on the roots of the corresponding characteristic equations, can reach nine. Also, the cases when the given integro-differential equation has a unique solution are found. The correctness of the obtained results with the help of the detailed solutions of concrete examples are shown. The method of solving the given problem can be used for solving model and nonmodel integro-differential equations with a higher order power singularity and logarithmic singularity in the kernel.

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25

Klamka, J., A. Babiarz, and M. Niezabitowski. "Banach fixed-point theorem in semilinear controllability problems – a survey." Bulletin of the Polish Academy of Sciences Technical Sciences 64, no. 1 (March 1, 2016): 21–35. http://dx.doi.org/10.1515/bpasts-2016-0004.

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Abstract The main aim of this article is to review the existing state of art concerning the complete controllability of semilinear dynamical systems. The study focus on obtaining the sufficient conditions for the complete controllability for various systems using the Banach fixedpoint theorem. We describe the results for stochastic semilinear functional integro-differential system, stochastic partial differential equations with finite delays, semilinear functional equations, a stochastic semilinear system, a impulsive stochastic integro-differential system, semilinear stochastic impulsive systems, an impulsive neutral functional evolution integro-differential system and a nonlinear stochastic neutral impulsive system. Finally, two examples are presented.

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26

Eidel'man, S. D., Alexey A. Chikriy, and Alexander G. Rurenko. "Linear Integro-Differential Games of Approach." Journal of Automation and Information Sciences 31, no. 1-3 (1999): 1–13. http://dx.doi.org/10.1615/jautomatinfscien.v31.i1-3.20.

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27

Guillen, Nestor, and Russell W. Schwab. "Neumann homogenization via integro-differential operators." Discrete and Continuous Dynamical Systems 36, no. 7 (March 2016): 3677–703. http://dx.doi.org/10.3934/dcds.2016.36.3677.

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28

Bijura, A. M. "Singularly Perturbed Volterra Integro-differential Equations." Quaestiones Mathematicae 25, no. 2 (June 2002): 229–48. http://dx.doi.org/10.2989/16073600209486011.

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29

Olach, Rudolf, and Helena Šamajová. "Oscillations of linear integro-differential equations." Central European Journal of Mathematics 3, no. 1 (March 2005): 98–104. http://dx.doi.org/10.2478/bf02475658.

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30

Cernea, Aurelian. "On a fractional integro-differential inclusion." Electronic Journal of Qualitative Theory of Differential Equations, no. 25 (2014): 1–11. http://dx.doi.org/10.14232/ejqtde.2014.1.25.

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31

Agarwal, R. P., Fu-Hsiang Wong, and Shiueh-Ling Yu. "Positive solutions of integro-differential inequalities." Computers & Mathematics with Applications 34, no. 10 (November 1997): 61–69. http://dx.doi.org/10.1016/s0898-1221(97)00207-1.

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32

Badr, A. A. "Integro-differential equation with Cauchy kernel." Journal of Computational and Applied Mathematics 134, no. 1-2 (September 2001): 191–99. http://dx.doi.org/10.1016/s0377-0427(00)00536-7.

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33

Garnier, Jimmy. "Accelerating Solutions in Integro-Differential Equations." SIAM Journal on Mathematical Analysis 43, no. 4 (January 2011): 1955–74. http://dx.doi.org/10.1137/10080693x.

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34

Prato, Giuseppe Da, and Alessandra Lunardi. "Stabilizability of integro-differential parabolic equations." Journal of Integral Equations and Applications 2, no. 2 (June 1990): 281–304. http://dx.doi.org/10.1216/jie-1990-2-2-281.

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35

Schikorra, Armin. "Integro-Differential Harmonic Maps into Spheres." Communications in Partial Differential Equations 40, no. 3 (October 27, 2014): 506–39. http://dx.doi.org/10.1080/03605302.2014.974059.

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36

Mustafa, Nizami. "Non-linear singular integro-differential equations." Complex Variables and Elliptic Equations 53, no. 9 (September 2008): 879–86. http://dx.doi.org/10.1080/17476930802187804.

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37

GRACE, Said R., and Ağacık ZAFER. "On oscillation of integro-differential equations." TURKISH JOURNAL OF MATHEMATICS 42 (2018): 204–10. http://dx.doi.org/10.3906/mat-1612-21.

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38

Ahmed, Hamdy, A. Hassan, and A. Ghanem. "Nonlinear Impulsive Fractional Integro Differential Equations." British Journal of Mathematics & Computer Science 10, no. 4 (January 10, 2015): 1–11. http://dx.doi.org/10.9734/bjmcs/2015/18725.

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39

Biazar, Jafar, and Mohammad Asadi. "Galerkin RBF for Integro-Differential Equations." British Journal of Mathematics & Computer Science 11, no. 2 (January 10, 2015): 1–9. http://dx.doi.org/10.9734/bjmcs/2015/19265.

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40

Tokmagambetov, Niyaz, and Berikbol T. Torebek. "Green's formula for integro-differential operators." Journal of Mathematical Analysis and Applications 468, no. 1 (December 2018): 473–79. http://dx.doi.org/10.1016/j.jmaa.2018.08.026.

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41

Robert, R., and S. M. Berleze. "Integro-differential equation of absorptive capacitors." IEEE Transactions on Dielectrics and Electrical Insulation 8, no. 2 (April 2001): 244–47. http://dx.doi.org/10.1109/94.919944.

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42

Chen, Yu-Bo, and Shouchuan Hu. "PBVP of volterra integro-differential equations." Applicable Analysis 22, no. 2 (July 1986): 133–37. http://dx.doi.org/10.1080/00036818608839611.

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43

Aristov, A. I. "On a nonclassical integro-differential equation." Differential Equations 51, no. 8 (August 2015): 1014–21. http://dx.doi.org/10.1134/s0012266115080054.

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44

Hoa, Ngo, Nguyen Phu, Tran Tung, and Le Quang. "Interval-valued functional integro-differential equations." Advances in Difference Equations 2014, no. 1 (2014): 177. http://dx.doi.org/10.1186/1687-1847-2014-177.

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45

Biswas, Anjan. "Integro-differential perturbations of optical solitons." Journal of Optics A: Pure and Applied Optics 2, no. 5 (July 3, 2000): 380–88. http://dx.doi.org/10.1088/1464-4258/2/5/306.

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46

Orlov, V. P. "On an abstract integro-differential problem." Mathematical Notes 66, no. 6 (December 1999): 733–40. http://dx.doi.org/10.1007/bf02674331.

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47

Shakhmurov, Veli, and Rishad Shahmurov. "Maximal B-regular integro-differential equation." Chinese Annals of Mathematics, Series B 30, no. 1 (January 2009): 39–50. http://dx.doi.org/10.1007/s11401-007-0553-9.

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48

Vasil’kovskaya, V. S., and A. V. Plotnikov. "Integro-differential systems with fuzzy noise." Ukrainian Mathematical Journal 59, no. 10 (October 2007): 1482–92. http://dx.doi.org/10.1007/s11253-008-0005-z.

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49

Plotnikov, A. V., and A. V. Tumbrukaki. "Integro-Differential Inclusions with Hukuhara Derivative." Nonlinear Oscillations 8, no. 1 (January 2005): 78–86. http://dx.doi.org/10.1007/s11072-005-0039-1.

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50

Ahmed, Hamdy M., and Mahmoud M. El-Borai. "Hilfer fractional stochastic integro-differential equations." Applied Mathematics and Computation 331 (August 2018): 182–89. http://dx.doi.org/10.1016/j.amc.2018.03.009.

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