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<p>This paper introduces a new iterative method to find fixed points of contractive mappings in uniformly convex Banach spaces. The method is proven to be stable and shows faster convergence than existing methods by Thakur, Piri, Ullah, and Harmouchi, as demonstrated through numerical examples and MATLAB plots. A detailed comparison highlights how different parameters affect convergence. We also establish a new result on data dependence using an approximate operator. Finally, the method is applied to solve a Caputo-type fractional differential equation, relevant to real-world problems in viscoelasticity, anomalous diffusion, and electrical circuits.</p>

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Approximating the solutions of fractional differential equations with a novel and more efficient iteration procedure

  • 期刊论文

  • 发表日期：

    2025年6月27日

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  • Khairul Habib Alam,
  • Yumnam Rohen,
  • Anita Tomar

摘要

This paper introduces a new iterative method to find fixed points of contractive mappings in uniformly convex Banach spaces. The method is proven to be stable and shows faster convergence than existing methods by Thakur, Piri, Ullah, and Harmouchi, as demonstrated through numerical examples and MATLAB plots. A detailed comparison highlights how different parameters affect convergence. We also establish a new result on data dependence using an approximate operator. Finally, the method is applied to solve a Caputo-type fractional differential equation, relevant to real-world problems in viscoelasticity, anomalous diffusion, and electrical circuits.