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<p>In this work, we study the existence, uniqueness, and stability of fractional stochastic pantograph differential equations involving the Caputo fractional derivative. By applying a fixed-point theorem under suitable assumptions, we establish sufficient conditions for the existence and uniqueness of solutions to the proposed equations. Additionally, we prove that the solution is Hyers-Ulam stable. Our results also provide a significant generalization of existing findings in the literature. Finally, a concrete example is presented to illustrate the effectiveness of the obtained results.</p>

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New techniques for the existence and stability of solutions to fractional stochastic pantograph differential equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月8日

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  • Rahman Ullah Khan,
  • Thabet Abdeljawad,
  • Bahaaeldin Abdalla

摘要

In this work, we study the existence, uniqueness, and stability of fractional stochastic pantograph differential equations involving the Caputo fractional derivative. By applying a fixed-point theorem under suitable assumptions, we establish sufficient conditions for the existence and uniqueness of solutions to the proposed equations. Additionally, we prove that the solution is Hyers-Ulam stable. Our results also provide a significant generalization of existing findings in the literature. Finally, a concrete example is presented to illustrate the effectiveness of the obtained results.