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Автор: Grafiati
Опубліковано: 14 березня 2023

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1

Kandemir, Mustafa. "SOLVABILITY OF BOUNDARY VALUE PROBLEMS WITH TRANSMISSION CONDITIONS FOR DISCONTINUOUS ELLIPTIC DIFFERENTIAL OPERATOR EQUATIONS." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 1 (March 30, 2016): 5842–57. http://dx.doi.org/10.24297/jam.v12i1.609.

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Анотація:
We consider nonlocal boundary value problems which includes discontinuous coefficients elliptic differential operator equations of the second order and nonlocal boundary conditions together with boundary-transmission conditions. We prove coerciveness and Fredholmness for these nonlocal boundary value problems.
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2

Bougoffa, Lazhar. "A third-order nonlocal problem with nonlocal conditions." International Journal of Mathematics and Mathematical Sciences 2004, no. 28 (2004): 1503–7. http://dx.doi.org/10.1155/s0161171204303017.

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Анотація:
We study an equation with dominated lower-order terms and nonlocal conditions. Using the Riesz representation theorem and the Schauder fixed-point theorem, we prove the existence and uniqueness of a generalized solution.
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3

Rossi, Julio D., and Carola-Bibiane Schönlieb. "Nonlocal higher order evolution equations." Applicable Analysis 89, no. 6 (June 2010): 949–60. http://dx.doi.org/10.1080/00036811003735824.

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4

Hache, Florian, Noël Challamel, and Isaac Elishakoff. "Asymptotic derivation of nonlocal beam models from two-dimensional nonlocal elasticity." Mathematics and Mechanics of Solids 24, no. 8 (March 29, 2018): 2425–43. http://dx.doi.org/10.1177/1081286518756947.

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Анотація:
The paper is focused on the possible justification of nonlocal beam models (at the macroscopic scale) from an asymptotic derivation based on nonlocal two-dimensional elasticity (at the material scale). The governing partial differential equations are expanded in Taylor series, through the dimensionless depth ratio of the beam. It is shown that nonlocal Bernoulli–Euler beam models can be asymptotically obtained from nonlocal two-dimensional elasticity, with a nonlocal length scale at the beam scale (macroscopic length scale) that may differ from the nonlocal length scale at the material scale. Only when the nonlocality is restricted to the axial direction are the two length scales coincident. In this specific nonlocal case, the nonlocal Bernoulli–Euler model emerged at the zeroth order of the asymptotic expansion, and the nonlocal truncated Bresse–Timoshenko model at the second order. However, in the general case, some new asymptotically-based nonlocal beam models are built which may differ from existing references nonlocal structural models. The natural frequencies for simply supported nonlocal beams are determined for each nonlocal model. The comparison shows that the models provide close results for low orders of frequencies and the difference increases with the order.
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5

Pavlačková, Martina, and Valentina Taddei. "Nonlocal semilinear second-order differential inclusions in abstract spaces without compactness." Archivum Mathematicum, no. 1 (2023): 99–107. http://dx.doi.org/10.5817/am2023-1-99.

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6

Nizhnik, Leonid. "Inverse spectral nonlocal problem for the first order ordinary differential equation." Tamkang Journal of Mathematics 42, no. 3 (August 24, 2011): 385–94. http://dx.doi.org/10.5556/j.tkjm.42.2011.881.

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7

Hou, Lijia, Yali Qin, Huan Zheng, Zemin Pan, Jicai Mei, and Yingtian Hu. "Hybrid High-Order and Fractional-Order Total Variation with Nonlocal Regularization for Compressive Sensing Image Reconstruction." Electronics 10, no. 2 (January 12, 2021): 150. http://dx.doi.org/10.3390/electronics10020150.

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Анотація:
Total variation often yields staircase artifacts in the smooth region of the image reconstruction. This paper proposes a hybrid high-order and fractional-order total variation with nonlocal regularization algorithm. The nonlocal means regularization is introduced to describe image structural prior information. By selecting appropriate weights in the fractional-order and high-order total variation coefficients, the proposed algorithm makes the fractional-order and the high-order total variation complement each other on image reconstruction. It can solve the problem of non-smooth in smooth areas when fractional-order total variation can enhance image edges and textures. In addition, it also addresses high-order total variation alleviates the staircase artifact produced by traditional total variation, still smooth the details of the image and the effect is not ideal. Meanwhile, the proposed algorithm suppresses painting-like effects caused by nonlocal means regularization. The Lagrange multiplier method and the alternating direction multipliers method are used to solve the regularization problem. By comparing with several state-of-the-art reconstruction algorithms, the proposed algorithm is more efficient. It does not only yield higher peak-signal-to-noise ratio (PSNR) and structural similarity (SSIM) but also retain abundant details and textures efficiently. When the measurement rate is 0.1, the gains of PSNR and SSIM are up to 1.896 dB and 0.048 dB respectively compared with total variation with nonlocal regularization (TV-NLR).
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8

Jung, Woo-Young, and Sung-Cheon Han. "Nonlocal Elasticity Theory for Transient Analysis of Higher-Order Shear Deformable Nanoscale Plates." Journal of Nanomaterials 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/208393.

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Анотація:
The small scale effect on the transient analysis of nanoscale plates is studied. The elastic theory of the nano-scale plate is reformulated using Eringen’s nonlocal differential constitutive relations and higher-order shear deformation theory (HSDT). The equations of motion of the nonlocal theories are derived for the nano-scale plates. The Eringen’s nonlocal elasticity of Eringen has ability to capture the small scale effects and the higher-order shear deformation theory has ability to capture the quadratic variation of shear strain and consequently shear stress through the plate thickness. The solutions of transient dynamic analysis of nano-scale plate are presented using these theories to illustrate the effect of nonlocal theory on dynamic response of the nano-scale plates. On the basis of those numerical results, the relations between nonlocal and local theory are investigated and discussed, as are the nonlocal parameter, aspect ratio, side-to-thickness ratio, nano-scale plate size, and time step effects on the dynamic response. In order to validate the present solutions, the reference solutions are employed and examined. The results of nano-scale plates using the nonlocal theory can be used as a benchmark test for the transient analysis.
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9

Correa, Ernesto, and Arturo de Pablo. "Nonlocal operators of order near zero." Journal of Mathematical Analysis and Applications 461, no. 1 (May 2018): 837–67. http://dx.doi.org/10.1016/j.jmaa.2017.12.011.

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10

Cardinali, Tiziana, and Serena Gentili. "An existence theorem for a non-autonomous second order nonlocal multivalued problem." Studia Universitatis Babes-Bolyai Matematica 62, no. 1 (March 1, 2017): 101–17. http://dx.doi.org/10.24193/subbmath.2017.0008.

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11

Zhang, Li-Qin, та Wen-Xiu Ma. "Nonlocal PT-Symmetric Integrable Equations of Fourth-Order Associated with so(3, ℝ)". Mathematics 9, № 17 (2 вересня 2021): 2130. http://dx.doi.org/10.3390/math9172130.

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Анотація:
The paper aims to construct nonlocal PT-symmetric integrable equations of fourth-order, from nonlocal integrable reductions of a fourth-order integrable system associated with the Lie algebra so(3,R). The nonlocalities involved are reverse-space, reverse-time, and reverse-spacetime. All of the resulting nonlocal integrable equations possess infinitely many symmetries and conservation laws.
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12

Benchohra, Mouffak, and Mohammed Souid. "L1-solutions for implicit fractional order differential equations with nonlocal conditions." Filomat 30, no. 6 (2016): 1485–92. http://dx.doi.org/10.2298/fil1606485b.

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Анотація:
In this paper we study the existence of integrable solutions of the nonlocal problem for fractional order implicit differential equations with nonlocal condition. Our results are based on Schauder?s fixed point theorem and the Banach contraction principle fixed point theorem.
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13

Niu, Jun Chuan, C. W. Lim, and A. Y. T. Leung. "Analytical Model of Unconstrained Nonlocal Higher-Order Nano-Plates for Bending Analysis." Advanced Materials Research 97-101 (March 2010): 4193–96. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.4193.

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Анотація:
This paper presents a higher-order nonlocal plate model and its formulation for bending analysis of nanoplates via variational principle and virtual work approach based on Leung’s unconstrained higher-order plate theory and Eringen’s nonlocal continuum theory. Bending of the simply supported rectangular higher-order nano-plate is investigated in comparison with the lower-order plate models. The numerical examples show that nonlocal nanoscale parameters increase the deflections of the plate as the rotary inertia and the transverse shear deformation do.
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14

Avalishvili, Gia, and Mariam Avalishvili. "On nonclassical problems for first-order evolution equations." gmj 18, no. 3 (July 14, 2011): 441–63. http://dx.doi.org/10.1515/gmj.2011.0028.

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Анотація:
Abstract The present paper deals with nonclassical initial-boundary value problems for parabolic equations and systems and their generalizations in abstract spaces. Nonclassical problems with nonlocal initial conditions for an abstract first-order evolution equation with time-dependent operator are considered, the existence and uniqueness results are proved and the algorithm of approximation of nonlocal problems by a sequence of classical problems is constructed. Applications of the obtained general results to initial-boundary value problems for parabolic equations and systems are considered.
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15

Besenyei, Ádám. "On some nonlocal systems containing a parabolic PDE and a first order ODE." Mathematica Bohemica 135, no. 2 (2010): 133–41. http://dx.doi.org/10.21136/mb.2010.140690.

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16

Assanova, Anar, and Zhanibek Tokmurzin. "A NONLOCAL MULTIPOINT PROBLEM FOR A SYSTEM OF FOURTH-ORDER PARTIAL DIFFERENTIAL EQUATIONS." Eurasian Mathematical Journal 11, no. 3 (2020): 8–20. http://dx.doi.org/10.32523/2077-9879-2020-11-3-08-20.

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17

Belakroum, Kh, A. Ashyralyev, and A. Guezane-Lakoud. "A note on the nonlocal boundary value problem for a third order partial differential equation." Filomat 32, no. 3 (2018): 801–8. http://dx.doi.org/10.2298/fil1803801b.

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Анотація:
The nonlocal boundary-value problem for a third order partial differential equation in a Hilbert space with a self-adjoint positive definite operator is considered. Applying operator approach, the theorem on stability for solution of this nonlocal boundary value problem is established. In applications, the stability estimates for the solution of three nonlocal boundary value problems for third order partial differential equations are obtained.
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18

Afrouzi, Ghasem A., David Barilla, Giuseppe Caristi, and Shahin Moradi. "One solution for nonlocal fourth order equations." Boletim da Sociedade Paranaense de Matemática 40 (December 17, 2021): 1–13. http://dx.doi.org/10.5269/bspm.43178.

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Анотація:
A critical point result for differentiable functionals is exploited in order to prove that a suitable class of fourth-order boundary value problem of Kirchhoff-type possesses at least one weak solution under an asymptotical behavior of the nonlinear datum at zero. Some examples to illustrate the results are given.
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19

Yangari, Miguel. "Monotone systems involving variable-order nonlocal operators." Publicacions Matemàtiques 66 (January 1, 2022): 129–58. http://dx.doi.org/10.5565/publmat6612205.

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20

Byszewski, Ludwik, and Teresa Winiarska. "An abstract nonlocal second order evolution problem." Opuscula Mathematica 32, no. 1 (2012): 75. http://dx.doi.org/10.7494/opmath.2012.32.1.75.

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21

Benchohra, Mouffak, Juan J. Nieto, and Noreddine Rezoug. "Second order evolution equations with nonlocal conditions." Demonstratio Mathematica 50, no. 1 (December 20, 2017): 309–19. http://dx.doi.org/10.1515/dema-2017-0029.

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Анотація:
Abstract In this paper, we shall establish sufficient conditions for the existence of solutions for second order semilinear functional evolutions equation with nonlocal conditions in Fréchet spaces. Our approach is based on the concepts of Hausdorff measure, noncompactness and Tikhonoff’s fixed point theorem. We give an example for illustration.
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22

Tian, Xiaochuan, and Qiang Du. "A Class of High Order Nonlocal Operators." Archive for Rational Mechanics and Analysis 222, no. 3 (July 6, 2016): 1521–53. http://dx.doi.org/10.1007/s00205-016-1025-8.

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23

Benedetti, I., N. V. Loi, L. Malaguti, and V. Taddei. "Nonlocal diffusion second order partial differential equations." Journal of Differential Equations 262, no. 3 (February 2017): 1499–523. http://dx.doi.org/10.1016/j.jde.2016.10.019.

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24

Witman, David R., Max Gunzburger, and Janet Peterson. "Reduced-order modeling for nonlocal diffusion problems." International Journal for Numerical Methods in Fluids 83, no. 3 (July 18, 2016): 307–27. http://dx.doi.org/10.1002/fld.4269.

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25

Sharma, Surbhi, and Sangeeta Kumari. "Reflection of Plane Waves in Nonlocal Fractional-Order Thermoelastic Half Space." International Journal of Mathematics and Mathematical Sciences 2022 (November 21, 2022): 1–11. http://dx.doi.org/10.1155/2022/1223847.

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Анотація:
The problem of plane waves in nonlocal fractional-order thermoelasticity has been studied. We have considered the x-y plane for the governing equation of nonlocal fractional thermoelasticity and solved these governing equations to calculate the equation in terms of frequency. This frequency shows that three sets of waves exist, in which two are coupled and one is uncoupled. The reflection coefficient of plane waves for classical theory and LS theory has been calculated. The effect of phase speeds, specific losses, and attenuation coefficients with respect to the frequency and nonlocal parameter for the two theories (LS theory and the classical theory of thermoelasticity) has been studied numerically for all propagating waves, and the same has been plotted graphically and explained thoroughly.
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26

El-Sayed, A. M. A., E. M. Hamdallah, and Kh W. El-kadeky. "Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second-Order Functional Differential Equation." Abstract and Applied Analysis 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/489353.

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Анотація:
We study the existence of at least one monotonic positive solution for the nonlocal boundary value problem of the second-order functional differential equationx′′(t)=f(t,x(ϕ(t))),t∈(0,1), with the nonlocal condition∑k=1makx(τk)=x0,x′(0)+∑j=1nbjx′(ηj)=x1, whereτk∈(a,d)⊂(0,1),ηj∈(c,e)⊂(0,1), andx0,x1>0. As an application the integral and the nonlocal conditions∫adx(t)dt=x0,x′(0)+x(e)-x(c)=x1will be considered.
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27

Li, Qiuxiang, Mingfu Fu, and Banghua Xie. "Analyzing the Bond Behavior of Fiber-Reinforced Polymer (FRP) Bars Embedded in Engineered Cementitious Composites (ECCs) with the Nonlocal Continuum Rod Model." Mathematical Problems in Engineering 2020 (July 20, 2020): 1–12. http://dx.doi.org/10.1155/2020/1710364.

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Анотація:
In this study, a nonlocal elastic rod model is applied to analytically evaluate the bond behavior between fiber-reinforced polymer (FRP) bars and engineered cementitious composites (ECCs). The second-order differential equation, which is based on nonlocal elasticity theory, governs the bond behavior of the FRP bars along the bond length. The classical elasticity model is a special case of the nonlocal model. The solution of the second-order differential equation can be obtained by substituting three-stage linear bond stress-slip relationship of the FRP bars. The slip values (solution of the second-order differential equation) within the bond length calculated by the nonlocal continuum rod model are affected by the nonlocal parameter e0a. The results from a case study show that the maximum pullout force decreases when the nonlocal size effect is considered, thereby providing a closer approximation of the experimental data than the existing local model.
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28

Jaafri, F., A. Ayoujil, and M. Berrajaa. "On a bi-nonlocal fourth order elliptic problem." Proyecciones (Antofagasta) 40, no. 1 (February 1, 2021): 239–53. http://dx.doi.org/10.22199/issn.0717-6279-2021-01-0015.

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29

Denche, Mohamed. "Nonlocal boundary value problem for second order abstract elliptic differential equation." Abstract and Applied Analysis 4, no. 3 (1999): 153–68. http://dx.doi.org/10.1155/s1085337599000135.

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Анотація:
We establish conditions that guarantee Fredholm solvability in the Banach spaceLpof nonlocal boundary value problems for elliptic abstract differential equations of the second order in an interval. Moreover, in the spaceL2we prove in addition the coercive solvability, and the completeness of root functions (eigenfunctions and associated functions). The obtained results are then applied to the study of a nonlocal boundary value problem for Laplace equation in a cylindrical domain.
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30

Kozhanov, Aleksandr I. "Nonlocal Integro-Differential Equations of the Second Order with Degeneration." Mathematics 8, no. 4 (April 16, 2020): 606. http://dx.doi.org/10.3390/math8040606.

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Анотація:
We study the solvability for boundary value problems to some nonlocal second-order integro–differential equations that degenerate by a selected variable. The possibility of degeneration in the equations under consideration means that the statements of the corresponding boundary value problems have to change depending on the nature of the degeneration, while the nonlocality in the equations implies that the boundary conditions will also have a nonlocal form. For the problems under study, the paper provides conditions that ensure their well-posedness.
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31

Wu, Chih-Ping, and Yen-Jung Chen. "Cylindrical Bending Vibration of Multiple Graphene Sheet Systems Embedded in an Elastic Medium." International Journal of Structural Stability and Dynamics 19, no. 04 (April 2019): 1950035. http://dx.doi.org/10.1142/s0219455419500354.

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Анотація:
Based on the Eringen nonlocal elasticity theory and multiple time scale method, an asymptotic nonlocal elasticity theory is developed for cylindrical bending vibration analysis of simply-supported, [Formula: see text]-layered, and uniformly or nonuniformly-spaced, graphene sheet (GS) systems embedded in an elastic medium. Both the interactions between the top and bottom GSs and their surrounding medium and the interactions between each pair of adjacent GSs are modeled as one-parameter Winkler models with different stiffness coefficients. In the formulation, the small length scale effect is introduced to the nonlocal constitutive equations by using a nonlocal parameter. The nondimensionalization, asymptotic expansion, and successive integration mathematical processes are performed for a typical GS. After assembling the motion equations for each individual GS to form those of the multiple GS system, recurrent sets of motion equations can be obtained for various order problems. Nonlocal multiple classical plate theory (CPT) is derived as a first-order approximation of the current nonlocal plane strain problem, and the motion equations for higher-order problems retain the same differential operators as those of nonlocal multiple CPT, although with different nonhomogeneous terms. Some nonlocal plane strain solutions for the natural frequency parameters of the multiple GS system with and without being embedded in the elastic medium and their corresponding mode shapes are presented to demonstrate the performance of the asymptotic nonlocal elasticity theory.
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32

Almoneef, Areej A., Shreen El-Sapa, Kh Lotfy, A. El-Bary, and Abdulkafi M. Saeed. "Laser Short-Pulse Effect on Thermodiffusion Waves of Fractional Heat Order for Excited Nonlocal Semiconductor." Advances in Condensed Matter Physics 2022 (August 12, 2022): 1–15. http://dx.doi.org/10.1155/2022/1523059.

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Анотація:
In this work, the thermal effect of a laser pulse is taken into account when mechanical-thermodiffusion (METD) waves are studied. The nonlocal semiconductor material is used when interference between holes and electrons occurs. The fractional technique is applied on the heat equation according to the photo-thermoelasticity theory. The governing equations describe the photo-excitation processes according to the overlapping between the thermoelasticity and photothermal theories. The thermoelastic deformation (TD) and the electronic deformation (ED) for the dimensionless fields are taken in one dimension (1D). The Laplace transforms are applied to obtain the analytical solutions when some initial and boundary conditions are applied at the nonlocal surface. The complete nondimensional solutions of the main quantities are obtained according to some numerical simulation approximate during the inversion processes of Laplace transforms and Fourier expansion. The time-fractional order, nonlocal, and thermal memories are used to compare the wave propagations of the main fields and are discussed graphically for nonlocal silicon material.
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33

El-Sayed, A. M. A., and Hoda A. Fouad. "On a Coupled System of Stochastic Ito^-Differential and the Arbitrary (Fractional) Order Differential Equations with Nonlocal Random and Stochastic Integral Conditions." Mathematics 9, no. 20 (October 14, 2021): 2571. http://dx.doi.org/10.3390/math9202571.

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Анотація:
The fractional stochastic differential equations had many applications in interpreting many events and phenomena of life, and the nonlocal conditions describe numerous problems in physics and finance. Here, we are concerned with the combination between the three senses of derivatives, the stochastic Ito^-differential and the fractional and integer orders derivative for the second order stochastic process in two nonlocal problems of a coupled system of two random and stochastic differential equations with two nonlocal stochastic and random integral conditions and a coupled system of two stochastic and random integral conditions. We study the existence of mean square continuous solutions of these two nonlocal problems by using the Schauder fixed point theorem. We discuss the sufficient conditions and the continuous dependence for the unique solution.
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34

Zozulya, V. V. "Nonlocal theory of curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models." Curved and Layered Structures 4, no. 1 (September 26, 2017): 221–36. http://dx.doi.org/10.1515/cls-2017-0015.

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Анотація:
Abstract New models for plane curved rods based on linear nonlocal theory of elasticity have been developed. The 2-D theory is developed from general 2-D equations of linear nonlocal elasticity using a special curvilinear system of coordinates related to the middle line of the rod along with special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby, all equations of elasticity including nonlocal constitutive relations have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of local elasticity, a system of differential equations in terms of displacements for Fourier coefficients has been obtained. First and second order approximations have been considered in detail. Timoshenko’s and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear nonlocal theory of elasticity which are considered in a special curvilinear system of coordinates related to the middle line of the rod. The obtained equations can be used to calculate stress-strain and to model thin walled structures in micro- and nanoscales when taking into account size dependent and nonlocal effects.
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35

Ashyralyev, Allaberen, and Okan Gercek. "On the Second Order of Accuracy Stable Implicit Difference Scheme for Elliptic-Parabolic Equations." Abstract and Applied Analysis 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/230190.

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Анотація:
We are interested in studying a second order of accuracy implicit difference scheme for the solution of the elliptic-parabolic equation with the nonlocal boundary condition. Well-posedness of this difference scheme is established. In an application, coercivity estimates in Hölder norms for approximate solutions of multipoint nonlocal boundary value problems for elliptic-parabolic differential equations are obtained.
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36

Zhang, Pei, and Hai Qing. "On well-posedness of two-phase nonlocal integral models for higher-order refined shear deformation beams." Applied Mathematics and Mechanics 42, no. 7 (June 24, 2021): 931–50. http://dx.doi.org/10.1007/s10483-021-2750-8.

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Анотація:
AbstractDue to the conflict between equilibrium and constitutive requirements, Eringen’s strain-driven nonlocal integral model is not applicable to nanostructures of engineering interest. As an alternative, the stress-driven model has been recently developed. In this paper, for higher-order shear deformation beams, the ill-posed issue (i.e., excessive mandatory boundary conditions (BCs) cannot be met simultaneously) exists not only in strain-driven nonlocal models but also in stress-driven ones. The well-posedness of both the strain- and stress-driven two-phase nonlocal (TPN-StrainD and TPN-StressD) models is pertinently evidenced by formulating the static bending of curved beams made of functionally graded (FG) materials. The two-phase nonlocal integral constitutive relation is equivalent to a differential law equipped with two restriction conditions. By using the generalized differential quadrature method (GDQM), the coupling governing equations are solved numerically. The results show that the two-phase models can predict consistent scale-effects under different supported and loading conditions.
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37

Premalatha, K., R. Amuda, V. K. Chandrasekar, M. Senthilvelan, and M. Lakshmanan. "Impact of Nonlocal Interaction on Chimera States in Nonlocally Coupled Stuart–Landau Oscillators." Complex Systems 30, no. 4 (December 15, 2021): 513–24. http://dx.doi.org/10.25088/complexsystems.30.4.513.

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We investigate the existence of collective dynamical states in nonlocally coupled Stuart–Landau oscillators with symmetry breaking included in the coupling term. We find that the radius of nonlocal interaction and nonisochronicity parameter play important roles in identifying the swing of synchronized states through amplitude chimera states. Collective dynamical states are distinguished with the help of strength of incoherence. Different transition routes to multi-chimera death states are analyzed with respect to the nonlocal coupling radius. In addition, we investigate the existence of collective dynamical states including traveling wave state, amplitude chimera state and multi-chimera death state by introducing higher-order nonlinear terms in the system. We also verify the robustness of the given notable properties for the coupled system.
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38

You, Huaiqian, Xin Yang Lu, Nathaniel Trask, and Yue Yu. "An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems." ESAIM: Mathematical Modelling and Numerical Analysis 55 (2021): S811—S851. http://dx.doi.org/10.1051/m2an/2020058.

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In this paper we consider 2D nonlocal diffusion models with a finite nonlocal horizon parameter δ characterizing the range of nonlocal interactions, and consider the treatment of Neumann-like boundary conditions that have proven challenging for discretizations of nonlocal models. We propose a new generalization of classical local Neumann conditions by converting the local flux to a correction term in the nonlocal model, which provides an estimate for the nonlocal interactions of each point with points outside the domain. While existing 2D nonlocal flux boundary conditions have been shown to exhibit at most first order convergence to the local counter part as δ → 0, the proposed Neumann-type boundary formulation recovers the local case as O(δ2) in the L∞(Ω) norm, which is optimal considering the O(δ2) convergence of the nonlocal equation to its local limit away from the boundary. We analyze the application of this new boundary treatment to the nonlocal diffusion problem, and present conditions under which the solution of the nonlocal boundary value problem converges to the solution of the corresponding local Neumann problem as the horizon is reduced. To demonstrate the applicability of this nonlocal flux boundary condition to more complicated scenarios, we extend the approach to less regular domains, numerically verifying that we preserve second-order convergence for non-convex domains with corners. Based on the new formulation for nonlocal boundary condition, we develop an asymptotically compatible meshfree discretization, obtaining a solution to the nonlocal diffusion equation with mixed boundary conditions that converges with O(δ2) convergence.
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39

You, Huaiqian, XinYang Lu, Nathaniel Task, and Yue Yu. "An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 4 (June 18, 2020): 1373–413. http://dx.doi.org/10.1051/m2an/2019089.

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Анотація:
In this paper we consider 2D nonlocal diffusion models with a finite nonlocal horizon parameter δ characterizing the range of nonlocal interactions, and consider the treatment of Neumann-like boundary conditions that have proven challenging for discretizations of nonlocal models. We propose a new generalization of classical local Neumann conditions by converting the local flux to a correction term in the nonlocal model, which provides an estimate for the nonlocal interactions of each point with points outside the domain. While existing 2D nonlocal flux boundary conditions have been shown to exhibit at most first order convergence to the local counter part as δ → 0, the proposed Neumann-type boundary formulation recovers the local case as O(δ2) in the L∞ (Ω) norm, which is optimal considering the O(δ2) convergence of the nonlocal equation to its local limit away from the boundary. We analyze the application of this new boundary treatment to the nonlocal diffusion problem, and present conditions under which the solution of the nonlocal boundary value problem converges to the solution of the corresponding local Neumann problem as the horizon is reduced. To demonstrate the applicability of this nonlocal flux boundary condition to more complicated scenarios, we extend the approach to less regular domains, numerically verifying that we preserve second-order convergence for non-convex domains with corners. Based on the new formulation for nonlocal boundary condition, we develop an asymptotically compatible meshfree discretization, obtaining a solution to the nonlocal diffusion equation with mixed boundary conditions that converges with O(δ2) convergence.
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40

Ashyralyev, A., та Kh Belakroum. "A Stable Difference Scheme for a Third-Order Partial Differential Equation". Contemporary Mathematics. Fundamental Directions 64, № 1 (15 грудня 2018): 1–19. http://dx.doi.org/10.22363/2413-3639-2018-64-1-1-19.

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The nonlocal boundary-value problem for a third order partial differential equation in a Hilbert space H with a self-adjoint positive definite operator A is considered. A stable three-step difference scheme for the approximate solution of the problem is presented. The main theorem on stability of this difference scheme is established. In applications, the stability estimates for the solution of difference schemes of the approximate solution of three nonlocal boundary value problems for third order partial differential equations are obtained. Numerical results for oneand two-dimensional third order partial differential equations are provided.
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41

Kumar, Suman, and R. Sakthivel. "Constrained controllability of second order retarded nonlinear systems with nonlocal condition." IMA Journal of Mathematical Control and Information 37, no. 2 (March 13, 2019): 441–54. http://dx.doi.org/10.1093/imamci/dnz007.

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Abstract In this paper, the constrained controllability of the second order retarded nonlinear systems with nonlocal condition has been established by using the theory of cosine families and the generalized open mapping theorem. A new set of sufficient conditions for the constrained controllability of retarded nonlinear systems is established under the assumption that the associated linear system is controllable. By using the Banach fixed point theorem, the existence of mild solution for the considered system with nonlocal delay condition has been deduced. Finally, an example is provided to verify the effectiveness of the obtained theory.
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42

Kim, Yongchae, and Hiroyuki Kudo. "Nonlocal Total Variation Using the First and Second Order Derivatives and Its Application to CT image Reconstruction." Sensors 20, no. 12 (June 20, 2020): 3494. http://dx.doi.org/10.3390/s20123494.

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We propose a new class of nonlocal Total Variation (TV), in which the first derivative and the second derivative are mixed. Since most existing TV considers only the first-order derivative, it suffers from problems such as staircase artifacts and loss in smooth intensity changes for textures and low-contrast objects, which is a major limitation in improving image quality. The proposed nonlocal TV combines the first and second order derivatives to preserve smooth intensity changes well. Furthermore, to accelerate the iterative algorithm to minimize the cost function using the proposed nonlocal TV, we propose a proximal splitting based on Passty’s framework. We demonstrate that the proposed nonlocal TV method achieves adequate image quality both in sparse-view CT and low-dose CT, through simulation studies using a brain CT image with a very narrow contrast range for which it is rather difficult to preserve smooth intensity changes.
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43

Todorov, Todor. "A second order problem with nonlocal boundary conditions." Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics 10, no. 2 (2018): 71–74. http://dx.doi.org/10.5937/spsunp1802071t.

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44

Ludu, Andrei. "Nonlocal Symmetries for Time-Dependent Order Differential Equations." Symmetry 10, no. 12 (December 19, 2018): 771. http://dx.doi.org/10.3390/sym10120771.

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A new type of ordinary differential equation is introduced and discussed: time-dependent order ordinary differential equations. These equations are solved via fractional calculus by transforming them into Volterra integral equations of second kind with singular integrable kernel. The solutions of the time-dependent order differential equation represent deformations of the solutions of the classical (integer order) differential equations, mapping them into one-another as limiting cases. This equation can also move, remove or generate singularities without involving variable coefficients. An interesting symmetry of the solution in relation to the Riemann zeta function and Harmonic numbers is observed.
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45

He, Jia, Yong Liang, Bashir Ahmad та Yong Zhou. "Nonlocal Fractional Evolution Inclusions of Order α ∈ (1,2)". Mathematics 7, № 2 (24 лютого 2019): 209. http://dx.doi.org/10.3390/math7020209.

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This paper studies the existence of mild solutions and the compactness of a set of mild solutions to a nonlocal problem of fractional evolution inclusions of order α ∈ ( 1 , 2 ) . The main tools of our study include the concepts of fractional calculus, multivalued analysis, the cosine family, method of measure of noncompactness, and fixed-point theorem. As an application, we apply the obtained results to a control problem.
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46

Géronimi, C., M. R. Feix, and P. G. L. Leach. "Exponential nonlocal symmetries and nonnormal reduction of order." Journal of Physics A: Mathematical and General 34, no. 47 (November 21, 2001): 10109–17. http://dx.doi.org/10.1088/0305-4470/34/47/315.

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47

Sluis, W. M., and P. H. M. Kersten. "Nonlocal higher-order symmetries for the Federbush model." Journal of Physics A: Mathematical and General 23, no. 11 (June 7, 1990): 2195–204. http://dx.doi.org/10.1088/0305-4470/23/11/040.

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48

Bolojan (Nica), Octavia, and Radu Precup. "Implicit first order differential systems with nonlocal conditions." Electronic Journal of Qualitative Theory of Differential Equations, no. 69 (2014): 1–13. http://dx.doi.org/10.14232/ejqtde.2014.1.69.

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49

Mawhin, Jean, Bogdan Przeradzki, and Katarzyna Szymańska-Dȩbowska. "Second order systems with nonlinear nonlocal boundary conditions." Electronic Journal of Qualitative Theory of Differential Equations, no. 56 (2018): 1–11. http://dx.doi.org/10.14232/ejqtde.2018.1.56.

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50

Gao, Xinghui, Chengyun Zhang, Dong Tang, Hui Zheng, Daquan Lu, and Wei Hu. "High-order dark solitons in nonlocal nonlinear media." Journal of Modern Optics 60, no. 15 (September 2013): 1281–86. http://dx.doi.org/10.1080/09500340.2013.837976.

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