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Research Article | Open Access

Theoretical analysis of a class of φ-Caputo fractional differential equations in Banach space

Ma'mon Abu Hammad1, Oualid Zentar2,3, Shameseddin Alshorm1( ), Mohamed Ziane2,3, Ismail Zitouni2
Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan
Department of Mathematics, University of Tiaret, Tiaret, Algeria
Laboratoire de Recherche en Intelligence Artificielle et Systèmes (LRIAS), University of Tiaret, Algeria
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Abstract

A study of a class of nonlinear differential equations involving the φ-Caputo type derivative in a Banach space framework is presented. Weissinger's and Meir-Keeler's fixed-point theorems are used to achieve some quantitative results. Two illustrative examples are provided to justify the theoretical results.

Keywords

φ-Caputo derivativefixed point theoremHausdorff measure of noncompactness
CLC number: 26A33, 34A08, 47H08

References

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AIMS Mathematics
Volume 9 Issue 3,
March 2024
Pages 6411-6423
DOI: 10.3934/math.2024312

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Cite this article:
Abu Hammad M, Zentar O, Alshorm S, et al. Theoretical analysis of a class of φ-Caputo fractional differential equations in Banach space. AIMS Mathematics, 2024, 9(3): 6411-6423. https://doi.org/10.3934/math.2024312

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Received: 10 December 2023
Revised: 22 January 2024
Accepted: 23 January 2024
Published: 15 March 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)