Existence and k-Mittag-Leffler-Ulam-Hyers stability results of k-generalized psi-Hilfer boundary value problem

Abdelkrim Salim; Mouffak Benchohra; Jamal Eddine Lazreg; Gaston N'Gu'er'ekata

Abdelkrim Salim Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89 Sidi Bel Abbes 22000, Algeria
Mouffak Benchohra Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89 Sidi Bel Abbes 22000, Algeria
Jamal Eddine Lazreg Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89 Sidi Bel Abbes 22000, Algeria
Gaston N'Gu'er'ekata Morgan State University, 1700 E. Cold Spring Lane, Baltimore M.D. 21252, USA

Abstract

This paper deals with some existence, uniqueness and $k$-Mittag-Leffler-Ulam-Hyers stability results for a class of boundary value problem for implicit nonlinear fractional differential equations and $k$-generalized $\psi$-Hilfer fractional derivative. Suitable examples are given for justifying our results and addressing different specific cases of our problem.