Fundamental Results about the Fractional Integro-Differential Equation Described with Caputo Derivative

In this paper, we study the existence and uniqueness of mild solution fractional integro-differential with nonlocal initial condition described by Caputo operator. Note that here order derivative satisfies α ∈ 1 , 2 . The id="M2"> -resolvent operator in Banach space fixed point theorem has been utilized proof solution. We have established paper Hyers-Ulam stability considered equation. An illustrative example provided to support main findings paper.