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<p>This paper investigates the existence, uniqueness, and stability of solutions for fractional Volterra–Fredholm integro-differential equations with state-dependent delay, incorporating Caputo fractional derivative and semigroup of operators. Using Krasnoselskii’s fixed point theorem, the existence of solutions is established under specified conditions, while the Banach Contraction Principle ensures the uniqueness of the solutions. Ulam’s stability concept is applied to demonstrate the robustness of the solutions to perturbations. An example is included to illustrate the application of the theoretical results, and numerical analysis is performed to validate the theoretical findings and examine the convergence of the solutions. Additionally, graphical analysis is also performed to visualize the solutions and their behavior.</p>

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Existence, Uniqueness, and Stability Results of Fractional Volterra–Fredholm Integro-Differential Equations with State-Dependent Delay

  • 期刊论文

  • 发表日期：

    2025年1月17日

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  • Tharmalingam Gunasekar,
  • Prabakaran Raghavendran,
  • Kottakkaran Sooppy Nisar

摘要

This paper investigates the existence, uniqueness, and stability of solutions for fractional Volterra–Fredholm integro-differential equations with state-dependent delay, incorporating Caputo fractional derivative and semigroup of operators. Using Krasnoselskii’s fixed point theorem, the existence of solutions is established under specified conditions, while the Banach Contraction Principle ensures the uniqueness of the solutions. Ulam’s stability concept is applied to demonstrate the robustness of the solutions to perturbations. An example is included to illustrate the application of the theoretical results, and numerical analysis is performed to validate the theoretical findings and examine the convergence of the solutions. Additionally, graphical analysis is also performed to visualize the solutions and their behavior.