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

Authors

  • Laboratory of Mathematics, University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abb\`es 22000, Algeria
  • Laboratory of Mathematics, University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abb\`es 22000, Algeria
  • Laboratory of Mathematics, University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abb\`es 22000, Algeria
  • 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.

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Published

2023-08-23

Issue

Vol. 30 No. 3 (2023): Nonlinear Studies (NS)

Section

Articles

How to Cite

Existence and stability for nonlinear implicit Caputo-exponential type fractional differential equations with non-instantaneous impulses in Banach spaces. (2023). Nonlinear Studies, 30(3). https://www.nonlinearstudies.com/index.php/nonlinear/article/view/3338