Mouffak Benchohra and Soufyane Bouriah
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.