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In this study, we focus on a class of Volterra–Fredholm integro-differential equations (VFIDEs) of fractional order, where the fractional derivative is defined in the Caputo sense. We establish sufficient conditions for the existence of unique solutions to these VFIDEs, employing the Banach fixed-point theorem to derive the results. We apply an operator-based approach, utilizing the Laplace transform and a discrete modified Adomian decomposition method based on Bernstein polynomials, to approximate the solutions. We also investigate the convergence of the method and compare it with the Homotopy Perturbation Method (HPM) for the problem under consideration. Numerical examples are presented to support the theoretical findings.

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Qualitative Analysis and Numerical Investigation of a Class of Nonlinear Volterra–Fredholm Integro-Differential Equations of Fractional Order

  • 会议论文

  • 发表日期：

    2026年

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  • Bapan Ali Miah,
  • Mausumi Sen,
  • R. Murugan

摘要

In this study, we focus on a class of Volterra–Fredholm integro-differential equations (VFIDEs) of fractional order, where the fractional derivative is defined in the Caputo sense. We establish sufficient conditions for the existence of unique solutions to these VFIDEs, employing the Banach fixed-point theorem to derive the results. We apply an operator-based approach, utilizing the Laplace transform and a discrete modified Adomian decomposition method based on Bernstein polynomials, to approximate the solutions. We also investigate the convergence of the method and compare it with the Homotopy Perturbation Method (HPM) for the problem under consideration. Numerical examples are presented to support the theoretical findings.