Fuzzy neutral fractional integro-differential equation existence and stability results involving the Caputo fractional generalized Hukuhara derivative-Reference-Cited by-同舟云学术

Fuzzy neutral fractional integro-differential equation existence and stability results involving the Caputo fractional generalized Hukuhara derivative

Published:2024-01-09 Issue:0 Volume:0 Page:
ISSN:2752-2334
Container-title:Journal of Nonlinear, Complex and Data Science
language:en
Short-container-title:

Author:

El Ghazouani Aziz¹^ORCID,Abdou Amir Fouad Ibrahim¹,Elomari M’hamed¹,Melliani Said¹

Affiliation:

1. Laboratory of Applied Mathematics and Scientific Computing , Sultan Moulay Slimane University , Beni Mellal , Morocco

Abstract

Abstract In this paper, we investigate the existence and uniqueness solutions for a fuzzy Neutral fractional integro-differential equation with non-local conditions. First, we show the existence of solutions with the help of the Non-linear alternative for one-value function, as well as Krasnoselskii’s and Banach’s fixed point theorems. Moreover, we examine the generalized Ulam Hyers (GUH) and Ulam Hyers Rassias stability for our main problem. Finally, an example is presented to show the usability of our major results.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/jncds-2023-0059/pdf

Reference20 articles.

1. R. Hilfer, Applications of Fractional Calculus in Physics, Orlando, World Scientific, 1999.

2. J. J. Trujillo, et al.., Fractional Calculus: Models and Numerical Methods, vol. 5, France, World Scientific, 2016.

3. F. C. Meral, T. J. Royston, and R. Magin, “Fractional calculus in viscoelasticity: an experimental study,” Commun. Nonlinear Sci. Numer. Simulat., vol. 15, no. 4, pp. 939–945, 2010. https://doi.org/10.1016/j.cnsns.2009.05.004.

4. I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods Of their Solution and Some of their Applications, USA, Elsevier, 1998.

5. A. El ghazouani, et al.., “On the existence and uniqueness of fuzzy mild solution of fractional evolution equations,” Kragujev. J. Math., vol. 49, no. 6, pp. 949–966, 2025.