Nawal Bettayeb†, Abdelkrim Salim‡, Jamal Eddine Lazreg§, Mouffak Benchohra¶
This article is a subject of some results of the existence, uniqueness, and Ulam-Hyers stability of solutions for a class of implicit neutral fractional differential coupled systems involving the tempered ψ-Caputo fractional derivative with delay. The results are based on the Perov fixed-point theorem for contractions and the Krasnoselskii fixed-point theorem in generalized Banach spaces. Furthermore, the Ulam-Hyers stability of the proposed system is studied. To illustrate our results, we give an example.
Keywords: implicit neutral tempered ψ-Caputo fractional derivative, coupled system, existence, uniqueness, Ulam–Hyers stability, generalized Banach space, fixed point.
MSC: 26A33, 34A08, 34A34
DOI 10.56082/annalsarscimath.2025.2.55
† nawalbettayeb@gmail.com, Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abbes 22000, Algeria
‡ a.salim@univ-chlef.dz, Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abbes 22000, Algeria; Faculty of Technology, Hassiba Benbouali University of Chlef, P.O. Box 151, Chlef 02000, Algeria
§ lazregjamal@yahoo.fr, Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abbes 22000, Algeria
¶ benchohra@yahoo.com, Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abbes 22000, Algeria
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 17 no 2, 2025
