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 valueproblems of nonlinear hybrid first order Caputo fractionalintegro-differential equations. The main tool employed here is theKrasnoselskii and Banach fixed point theorems. An example is also given toillustrate the main results. In addition, the case of the Higher orderCaputo fractional integro-differential equations is studied.