Stability of some generalized fractional differential equations in the sense of Ulam-Hyers-Rassias

Abdellatif Ben Makhlouf; El-Sayed El-Hady; Hassen Arfaoui; Salah Boulaaras; Lassaad Mchiri

doi:10.1186/s13661-023-01695-5

Stability of some generalized fractional differential equations in the sense of Ulam-Hyers-Rassias

Bound Value Probl. 2023;2023(1):8. doi: 10.1186/s13661-023-01695-5. Epub 2023 Jan 26.

Authors

Abdellatif Ben Makhlouf¹, El-Sayed El-Hady¹, Hassen Arfaoui¹, Salah Boulaaras², Lassaad Mchiri^{3

4}

Affiliations

¹ Mathematics Department, College of Science, Jouf University, P.O. Box: 2014, Sakaka, Saudi Arabia.
² Department of Mathematics, College of Sciences and Arts, ArRass, Qassim University, Buraydah, Saudi Arabia.
³ Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Route Soukra, BP 1171, 3000 Sfax, Tunisia.
⁴ ENSIIE, University of Evry-Val-d'Essonne, 1 square de la Résistance, 91025 Évry-Courcouronnes Cedex, France.

Abstract

In this paper, we investigate the existence and uniqueness of fractional differential equations (FDEs) by using the fixed-point theory (FPT). We discuss also the Ulam-Hyers-Rassias (UHR) stability of some generalized FDEs according to some classical mathematical techniques and the FPT. Finally, two illustrative examples are presented to show the validity of our results.

Keywords: Fixed-point theory; Generalized fractional differential equation; Hyers–Ulam–Rassias stability.