• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권1호
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• pp.19-38
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• 2006

We analyze the spectral collocation approximation for a parabolic partial integrodifferential equations(PIDE) with a weakly singular kernel. The space discretization is based on the spectral collocation method and the time discretization is based on Crank-Nicolson scheme with a graded mesh. We obtain the stability and second order convergence result for fully discrete scheme.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.415-425
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• 2005

This paper outlines a reliable strategy for solving nonlinear Volterra-Fredholm integro-differential equations. The modified form of Adomian decomposition method is found to be fast and accurate. Numerical examples are presented to illustrate the accuracy of the method.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1145-1156
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• 2009

In this paper, we consider the existence, uniqueness of the solutions and controllability for the neutral functional integro-differential equations with delay terms by Sadovskii's fixed point theorem.

• Korean Journal of Mathematics
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• 제13권2호
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• pp.149-159
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• 2005

We study an age-dependent s-i-s epidemic model with spatial diffusion. The model equations are described by a nonlinear and nonlocal system of integro-differential equations. Finite difference methods along the characteristics in age-time domain combined with finite elements in the spatial variable are applied to approximate the solution of the model. Stability of the discrete periodic solution is investigated.

• Kyungpook Mathematical Journal
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• 제28권2호
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• pp.177-183
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• 1988

In this work, two numerical schemes arc proposed for solving a general form of Cauchy problem. Here, the problem, to be defined, consists of a system of Volterra integro-differential equations. Picard's and Seiddl'a methods of successive approximations are ued to obtain the approximate solution. The convergence of these approximations is established and the rate of convergence is estimated in every case.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.1089-1103
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• 2022

This paper focuses on the existence and uniqueness outcome for fractional integro-differential equation (FIDE) among impulsive edge condition and Hyers-Ulam-Rassias Stability (HURS) by using fractional calculus and some fixed point theorem in some weak conditions. The outcome procured in this paper upgrade and perpetuate some studied solutions.

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.237-249
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• 2023

In this paper, by means of the Schauder fixed point theorem and Arzela-Ascoli theorem, the existence and uniqueness of solutions for a class of not instantaneous impulsive problems of nonlinear fractional functional Volterra-Fredholm integro-differential equations are investigated. An example is given to illustrate the main results.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.851-863
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• 2023

We study the appropriate conditions for the findings of uniqueness and existence for a group of boundary value problems for impulsive Ψ-Caputo fractional nonlinear Volterra-Fredholm integro-differential equations (V-FIDEs) with symmetric boundary non-instantaneous conditions in this paper. The findings are based on the fixed point theorem of Krasnoselskii and the Banach contraction principle. Finally, the application is provided to validate our primary findings.

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.407-420
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• 2023

In this manuscript, we study the sufficient conditions for controllability of Volterra-Fredholm type fractional integro-differential systems in a Banach space. Fractional calculus and the fixed point theorem are used to derive the findings. Some examples are provided to illustrate the obtained results.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.259-273
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• 2024

In this manuscript, we study the sufficient conditions for existence and uniqueness results of solutions of impulsive Hilfer fractional Volterra-Fredholm integro-differential equations with integral boundary conditions. Fractional calculus and Banach contraction theorem used to prove the uniqueness of results. Moreover, we also establish Hyers-Ulam stability for this problem. An example is also presented at the end.