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<p>We address the solvability of an infinite system of Riemann–Liouville fractional integral equations. We begin by establishing the system and then explore the existence of solutions using the Meir–Keeler condensing operator technique. To demonstrate the applicability of our theoretical findings, some illustrative examples are presented. In addition, we propose an iterative algorithm that combines the Adomian Decomposition Method with a modified Homotopy Perturbation Method to approximate solutions for the system. The effectiveness of the proposed approach is further validated through these examples, offering a practical means of estimating solutions to the infinite system.</p>

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A study on solvability and an iterative method for infinite systems of fractional integro-differential equations

  • 期刊论文

  • 发表日期：

    2025年5月7日

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  • Rahul Rahul,
  • Sukanta Halder,
  • Manochehr Kazemi,
  • Mohammad Esmael Samei

摘要

We address the solvability of an infinite system of Riemann–Liouville fractional integral equations. We begin by establishing the system and then explore the existence of solutions using the Meir–Keeler condensing operator technique. To demonstrate the applicability of our theoretical findings, some illustrative examples are presented. In addition, we propose an iterative algorithm that combines the Adomian Decomposition Method with a modified Homotopy Perturbation Method to approximate solutions for the system. The effectiveness of the proposed approach is further validated through these examples, offering a practical means of estimating solutions to the infinite system.