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<p>Generalized boundary value problems (BVP) typically cover a wide range of equations. In this study, we focus on a generalization of Caputo-type fractional discrete differential equations that involve two or more fractional <i>q</i>-integrals. We analyze the existence and uniqueness of solutions to the multi-point nonlinear BVP based on several fixed point theorems, including the Banach fixed point theorem, the nonlinear Leray-Schauder alternative, and the Leray-Schauder degree theory. Finally, several examples are presented to illustrate the accuracy of our results.</p>

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Existence of solutions to a fractional differential equation involving the Caputo q-derivative with boundary conditions in Banach spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月30日

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  • Houari Bouzid,
  • Benali Abdelkader,
  • Louiza Tabharit,
  • Mohammad Esmael Samei

摘要

Generalized boundary value problems (BVP) typically cover a wide range of equations. In this study, we focus on a generalization of Caputo-type fractional discrete differential equations that involve two or more fractional q-integrals. We analyze the existence and uniqueness of solutions to the multi-point nonlinear BVP based on several fixed point theorems, including the Banach fixed point theorem, the nonlinear Leray-Schauder alternative, and the Leray-Schauder degree theory. Finally, several examples are presented to illustrate the accuracy of our results.