Existence and Hyers–Ulam stability of solutions to a nonlinear implicit coupled system of fractional order

Abstract In this typescript, we study system of nonlinear implicit coupled differential equations of arbitrary (non–integer) order having nonlocal boundary conditions on closed interval [0, 1] with Caputo fractional derivative. We establish sufficient conditions for the existence, at least one and a unique solution of the proposed coupled system with the help of Krasnoselskii’s fixed point theorem and Banach contraction principle. Moreover, we scrutinize the Hyers–Ulam stability for the considered problem. We present examples to illustrate our main results.