Existence and uniqueness of Solution for Boundary Value Problem of Fractional Order

In this study, we investigate a class of fractional ordering and fractional derivative-based boundary value problems.   and . There are four boundary value requirements in this equation. The Banach fixed point theorem (Contraction mapping theorem) and the Schauder fixed point theorem are both used to arrive at the existence and uniqueness solution. Examples based on the fractional integral method and integral operator are used to illustrate our main points.