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<p>This paper explores a novel numerical iterative approach for approximating solutions of Volterra type integral equations involving fractional order derivative, based on the methods of successive approximations and the product Simpson integration. We consider certain conditions regarding the existence and uniqueness of the solution along with estimate of the error approximations. Further, regarding of the proposed method, we try to examine both of the convergence analysis and numerical stability. In the end, two illustrative examples demonstrate the theoretical achievements.</p>

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The product Simpson method: excellent estimating solution of fractional integral equations via uniformly modulus of continuity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月29日

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  • Manochehr Kazemi,
  • Mohammad Esmael Samei,
  • Mohamed M. A. Metwali,
  • Shami A. M. Alsallami

摘要

This paper explores a novel numerical iterative approach for approximating solutions of Volterra type integral equations involving fractional order derivative, based on the methods of successive approximations and the product Simpson integration. We consider certain conditions regarding the existence and uniqueness of the solution along with estimate of the error approximations. Further, regarding of the proposed method, we try to examine both of the convergence analysis and numerical stability. In the end, two illustrative examples demonstrate the theoretical achievements.