Mouffak Benchohra and Soufyane Bouriah

Existence and Stability Results for Nonlinear Implicit Fractional Differential Equations with Impulses

abstract:
In this paper, we establish the existence and uniqueness of solutions for a class of boundary value problems for nonlinear implicit fractional differential equations with impulse and Caputo's fractional derivatives, the stability of this class of problems is considered, as well. The arguments are based upon the Banach contraction principle and the Schaefer's fixed point theorem. We present two examples to show the applicability of our results.

Mathematics Subject Classification: 26A33, 34A08, 34A37

Key words and phrases: Boundary value problem, Caputo's fractional derivative, implicit fractional differential equations, fractional integral, existence, stability, fixed point, impulses.