Existence and numerical solutions of a coupled system of integral BVP for fractional differential equations

This paper is devoted to establishing the existence theory for at least one solution to a coupled system of fractional order differential equations (FDEs). The problem under consideration is subjected to movable type integral boundary conditions over a finite time interval. Furthermore, we investigate the approximate solutions to the considered problem with the help of the differential transform. Moreover, some necessary conditions for the Hyers-Ulam type stability to the solution of the proposed problem are developed. The whole investigation has been illustrated by providing some suitable examples.