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<p>In this paper, new results on existence and uniqueness of solutions for Hilfer fractional differential equations under impulsive delay conditions are obtained using the fixed-point approach. Existence of solutions is proven using Krasnoselskii’s fixed-point theorem, and uniqueness is proven using the Banach contraction principle. Compared to most other related works where the study was confined to fractional differential equations using either Caputo- or Riemann–Liouville-type derivative with relatively less complex delay, in this paper, we have considered Hilfer-type derivative together with impulsive conditions as well as indefinite delay. Thus, our results not only generalize but also unify some known results. As an application, four examples are included.</p>

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Existence and uniqueness results for solutions of Hilfer fractional differential equations with impulsive delay conditions via fixed-point technique

  • 期刊论文

  • 发表日期：

    2026年7月14日

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  • Natasha Irshad,
  • Rahim Shah

摘要

In this paper, new results on existence and uniqueness of solutions for Hilfer fractional differential equations under impulsive delay conditions are obtained using the fixed-point approach. Existence of solutions is proven using Krasnoselskii’s fixed-point theorem, and uniqueness is proven using the Banach contraction principle. Compared to most other related works where the study was confined to fractional differential equations using either Caputo- or Riemann–Liouville-type derivative with relatively less complex delay, in this paper, we have considered Hilfer-type derivative together with impulsive conditions as well as indefinite delay. Thus, our results not only generalize but also unify some known results. As an application, four examples are included.