Theoretical analysis of a class of $ \varphi $-Caputo fractional differential equations in Banach space

Ma'mon Abu Hammad; Oualid Zentar; Shameseddin Alshorm; Mohamed Ziane; Ismail Zitouni; Ma'mon Abu Hammad; Oualid Zentar; Shameseddin Alshorm; Mohamed Ziane; Ismail Zitouni

doi:10.3934/math.2024312

AIMS Mathematics

2024, Volume 9, Issue 3: 6411-6423. doi: 10.3934/math.2024312

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Theoretical analysis of a class of $ \varphi $-Caputo fractional differential equations in Banach space

1.
Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan
2.
Department of Mathematics, University of Tiaret, Tiaret, Algeria
3.
Laboratoire de Recherche en Intelligence Artificielle et Systèmes (LRIAS), University of Tiaret, Algeria

Received: 10 December 2023 Revised: 22 January 2024 Accepted: 23 January 2024 Published: 05 February 2024
MSC : 26A33, 34A08, 47H08

A study of a class of nonlinear differential equations involving the $ \varphi $-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.
- $ \varphi $-Caputo derivative,
- fixed point theorem,
- Hausdorff measure of noncompactness
Citation: Ma'mon Abu Hammad, Oualid Zentar, Shameseddin Alshorm, Mohamed Ziane, Ismail Zitouni. Theoretical analysis of a class of $ \varphi $-Caputo fractional differential equations in Banach space[J]. AIMS Mathematics, 2024, 9(3): 6411-6423. doi: 10.3934/math.2024312

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Abstract

A study of a class of nonlinear differential equations involving the $ \varphi $-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.

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