Existence and stability for nonlinear implicit Caputo-exponential type fractional differential equations with non-instantaneous impulses in Banach spaces

Ahmed Ilyes N. Malti; Jamal Eddine Lazreg; Mouffak Benchohra; Gaston Mandata N'Gu\'er\'ekata

Ahmed Ilyes N. Malti Laboratory of Mathematics, University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abb\`es 22000, Algeria
Jamal Eddine Lazreg Laboratory of Mathematics, University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abb\`es 22000, Algeria
Mouffak Benchohra Laboratory of Mathematics, University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abb\`es 22000, Algeria
Gaston Mandata N'Gu\'er\'ekata NEERLab, Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore M.D. 21252, USA

Abstract

In this paper, we investigate the existence of solutions and Ulam-Hyers-Rassias stability for a class of initial value problem for nonlinear implicit fractional differential equations with non-instantaneous impulses involving Caputo--Exponential fractional derivative. The existence results are obtained by using the technique of measure of noncompactness and the fixed point theorems of Darbo and M\"onch. In the paper a generalization to nonlocal condition is indicated. Several enlightening examples are also presented.