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<p>In this article, we investigate the existence and uniqueness of solutions for fractional-order two-dimensional Volterra-type nonlinear integro-differential equations with delay. The existence of solutions is established using Krasnoselskii’s fixed point theorem, while the uniqueness is proven with the help of Banach’s fixed point theorem. Furthermore, numerical solutions are obtained using the discrete Laplace Adomian decomposition method for the considered class of integro-differential equations. Several numerical examples are presented to validate the theoretical findings.</p>

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Existence and Uniqueness Result for Two-Dimensional Fraction Order Nonlinear IDE with Delay and Its Numerical Investigation

  • 期刊论文

  • 发表日期：

    2025年3月21日

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

摘要

In this article, we investigate the existence and uniqueness of solutions for fractional-order two-dimensional Volterra-type nonlinear integro-differential equations with delay. The existence of solutions is established using Krasnoselskii’s fixed point theorem, while the uniqueness is proven with the help of Banach’s fixed point theorem. Furthermore, numerical solutions are obtained using the discrete Laplace Adomian decomposition method for the considered class of integro-differential equations. Several numerical examples are presented to validate the theoretical findings.