Proving The Existence and the Uniqueness Solutions of fractional Integro-Differential Equations

In this paper, we will study and prove the existence and the uniqueness theorems of solutions of the generalized linear integro-differential equations with unequal fractional order of differentiation and integration by using Schauder fixed point theorem. This type of fractional integro-differential equation may be considered as a generalization to the other types of fractional integro-differential equations Considered by other researchers, as well as, to the usual integro-differential equations.