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

Qun Dai; Shidong Liu; Qun Dai; Shidong Liu

doi:10.3934/math.2022140

AIMS Mathematics

2022, Volume 7, Issue 2: 2498-2511. doi: 10.3934/math.2022140

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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

Received: 05 September 2021 Accepted: 31 October 2021 Published: 15 November 2021
MSC : 34A08, 34D20, 34K37, 47H10

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.
- mixed Caputo fractional derivative,
- weighted space method,
- Ulam-Hyers stability,
- Ulam-Hyers-Rassias stability,
- semi-Ulam-Hyers-Rassias stability
Citation: Qun Dai, Shidong Liu. Stability of the mixed Caputo fractional integro-differential equation by means of weighted space method[J]. AIMS Mathematics, 2022, 7(2): 2498-2511. doi: 10.3934/math.2022140

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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.

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