Existence and uniqueness theorems for nonlinear coupled boundary value problem of the A B C fractional differential equation

‎In this paper‎, ‎we study existence and uniqueness of solutions for a new systems of nonlinear coupled boundary value problem of the \(\mathcal{ABC}\) fractional differential equation‎. ‎By applying the Banach's‎ ‎fixed point theorem and Krasnoselskii's fixed point theorem‎, ‎the existence of solutions is obtained‎. ‎Further‎, ‎the provided problem Ulam-Hyers (\(\mathcal{UH}\)) and generalized Ulam-Hyers (\(\mathcal{GUH}\)) stability are both investigated‎. ‎The result obtained in this work are well illustrated with the aid of examples‎.