<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, we are concerned with a class of nonlinear fractional differential equation with delays. By means of the contraction mapping principle, we prove the existence of a unique solution and investigate the continuous dependence of the solution upon the initial data and two types of Ulam stability: Ulam-Hyers and Ulam-Hyers-Rassias ones. Then, we give an example to illustrate the main results.</p>
</abstract>

In this paper, we are concerned with a class of nonlinear fractional differential equation with delays. By means of the contraction mapping principle, we prove the existence of a unique solution and investigate the continuous dependence of the solution upon the initial data and two types of Ulam stability: Ulam-Hyers and Ulam-Hyers-Rassias ones. Then, we give an example to illustrate the main results.

Existence and stability for a semilinear fractional differential equation with two delays

Department of Mathematics, Faculty of Sciences

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this paper, we are concerned with a class of nonlinear fractional differential equation with delays. By means of the contraction mapping principle, we prove...

Existence and stability for a semilinear fractional differential equation with two delays

Published Online: Jun 20, 2022

Page range: 111 - 125

DOI: https://doi.org/10.2478/awutm-2022-0009

Keywords
Fractional differential equation, discrete delay, existence of solution, continuous dependence upon initial data, Ulam stability, contraction mapping principle

© 2022 Rahima Atmania, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Existence and stability for a semilinear fractional differential equation with two delays

Published Online: Jun 20, 2022

Page range: 111 - 125

DOI: https://doi.org/10.2478/awutm-2022-0009

KeywordsFractional differential equation, discrete delay, existence of solution, continuous dependence upon initial data, Ulam stability, contraction mapping principle

© 2022 Rahima Atmania, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Fractional differential equation, discrete delay, existence of solution, continuous dependence upon initial data, Ulam stability, contraction mapping principle