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Research Article | Open Access

Existence and Ulam stability for fractional differential equations of mixed Caputo-Riemann derivatives

Shayma A. Murad, Zanyar A. Ameen( )
Department of Mathematics, College of Science, University of Duhok, Duhok 42001, IRAQ
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Abstract

In this paper, we study the existence, uniqueness, and stability theorems of solutions for a differential equation of mixed Caputo-Riemann fractional derivatives with integral initial conditions in a Banach space. Our analysis is based on an application of the Shauder fixed point theorem with Ulam-Hyers and Ulam-Hyers-Rassias theorems. A couple of examples are presented to illustrate the obtained results.

Keywords

fractional differential equationRiemann and Caputo fractional derivativesfixed point theoremstability analysis
CLC number: 26A33, 34A08, 34A12, 34B27, 34D20, 34K20

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AIMS Mathematics
Volume 7 Issue 4,
April 2022
Pages 6404-6419
DOI: 10.3934/math.2022357

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Cite this article:
Murad SA, Ameen ZA. Existence and Ulam stability for fractional differential equations of mixed Caputo-Riemann derivatives. AIMS Mathematics, 2022, 7(4): 6404-6419. https://doi.org/10.3934/math.2022357

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Received: 07 October 2021
Revised: 17 November 2021
Accepted: 05 December 2021
Published: 15 April 2022
©2022 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)