Existence and uniqueness of mild solutions for nonlinear hybrid Caputo fractional integro-differential equations via fixed point theorems

Abstract

We prove the existence and uniqueness of mild solutions for initial value problems of nonlinear hybrid first order Caputo fractional integro-differential equations. The main tool employed here is the Krasnoselskii and Banach fixed point theorems. An example is also given to illustrate the main results. In addition, the case of the Higher order Caputo fractional integro-differential equations is studied.

Keywords

• fixed point theorems
• existence
• uniqueness
• hybrid fractional integro-differential equations