Existence results for a nonlinear coupled system involving both Caputo and Riemann–Liouville generalized fractional derivatives and coupled integral boundary conditions

Abstract

In this paper, we investigate the existence of solutions for a nonlinear fractional-order coupled system involving both Caputo and Riemann–Liouville generalized fractional derivatives of different orders equipped with coupled integral boundary conditions. We transform the given system into an equivalent fixed point problem and solve it by applying the standard fixed point theorems. Examples are constructed for the illustration of the obtained results.