ON A TYPE OF DIFFERENTIAL CALCULUS IN THE FRAME OF GENERALIZED HILFER INTEGRO-DIFFERENTIAL EQUATION

Abstract

In this paper, we investigate the existence and uniqueness of solutions to anew class of integro-differential equation boundary value problems (BVPs) with T-Hilferoperator. Our problem is converted into an equivalent fixed-point problem by introducingan operator whose fixed points coincide with the solutions to the given problem. UsingBanach's and Schauder's fixed point techniques, the uniqueness and existence result for thegiven problem are demonstrated. The stability results for solutions of the given problem arealso discussed. In the end. One example is provided to demonstrate the obtained results