Impulsive boundary value problems for nonlinear implicit Caputo-exponential type fractional differential equations

Abstract

This paper deals with existence and uniqueness of solutions to a class of impulsive boundary value problem for nonlinear implicit fractional differential equations involving the Caputo-exponential fractional derivative. The existence results are based on Schaefer's fixed point theorem and the uniqueness result is established via Banach's contraction principle. Two examples are given to illustrate the main results.

Keywords

• boundary value problem
• caputo-exponential fractional derivative
• implicit fractional differential equations
• existence
• fixed point
• impulses