A Caputo-Type Fractional Derivative of a Function with Respect to Power Functions and Solutions to Non-Local Problems of Fractional Differential Equations

This paper investigates the uniform continuity and strong continuity of the semigroups of the fractional integral operators of power functions. Using the Krasnoselskii’s fixed-point theorem, we have studied the non-local problem related to fractional differential equations involving power functions with multi-point integral boundary conditions and obtain the existence of the solution.