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Research Article | Open Access

Stability of the mixed Caputo fractional integro-differential equation by means of weighted space method

Qun Dai, Shidong Liu( )
School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun 130022, China
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Abstract

In this research work, we consider a class of nonlinear fractional integro-differential equations containing Caputo fractional derivative and integral derivative. We discuss the stabilities of Ulam-Hyers, Ulam-Hyers-Rassias, semi-Ulam-Hyers-Rassias for the nonlinear fractional integro-differential equations in terms of weighted space method and Banach fixed-point theorem. After the demonstration of our results, an example is given to illustrate the results we obtained.

Keywords

mixed Caputo fractional derivativeweighted space methodUlam-Hyers stabilityUlam-Hyers-Rassias stabilitysemi-Ulam-Hyers-Rassias stability
CLC number: 34A08, 34D20, 34K37, 47H10

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AIMS Mathematics
Volume 7 Issue 2,
February 2022
Pages 2498-2511
DOI: 10.3934/math.2022140

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Cite this article:
Dai Q, Liu S. Stability of the mixed Caputo fractional integro-differential equation by means of weighted space method. AIMS Mathematics, 2022, 7(2): 2498-2511. https://doi.org/10.3934/math.2022140

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Received: 05 September 2021
Accepted: 31 October 2021
Published: 15 February 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)