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<p>In this study, we establish existence and Ulam-Hyers results for nonlinear sequential fractional differential equations involving the deformable derivative. We employ the Banach contraction principle and Krasnoselskii’s theorem to achieve these results. A key novelty of this work lies in the use of a sequential application of the deformable derivative, which yields a richer mathematical structure compared to single-order formulations. The theoretical findings are illustrated through a concrete example, and the practical relevance of the results is discussed in the context of stability analysis for dynamical systems modeled by deformable fractional equations.</p>

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Existence results and Ulam-Hyers stability for a sequential deformable fractional initial value problem

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月19日

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  • Leila Slimane,
  • Souad Ayadi,
  • Ozgur Ege,
  • Ahmad Aloqaily,
  • Nabil Mlaiki

摘要

In this study, we establish existence and Ulam-Hyers results for nonlinear sequential fractional differential equations involving the deformable derivative. We employ the Banach contraction principle and Krasnoselskii’s theorem to achieve these results. A key novelty of this work lies in the use of a sequential application of the deformable derivative, which yields a richer mathematical structure compared to single-order formulations. The theoretical findings are illustrated through a concrete example, and the practical relevance of the results is discussed in the context of stability analysis for dynamical systems modeled by deformable fractional equations.