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

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

Abstract 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...

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Bibliographic Details
Main Authors: Houari Bouzid, Benali Abdelkader, Louiza Tabharit, Mohammad Esmael Samei
Format: Article
Language:English
Published: SpringerOpen 2025-04-01
Series:Journal of Inequalities and Applications
Subjects:
Nonlinear fractional equation
Leray-Schauder alternative
Existence
Riemann–Liouville q-integral
Online Access:https://doi.org/10.1186/s13660-025-03302-w
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Summary:Abstract 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.
ISSN:1029-242X

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