EXISTENCE AND STABILITY THEORIES FOR A COUPLED SYSTEM INVOLVING p-LAPLACIAN OPERATOR OF A NONLINEAR ATANGANA–BALEANU FRACTIONAL DIFFERENTIAL EQUATIONS

We investigate the appropriate and sufficient conditions for the existence and uniqueness of a solution for a coupled system of Atangana–Baleanu fractional equations with a p-Laplacian operator. We also study the HU-stability of the solution by using the Atangana–Baleanu–Caputo (ABC) derivative. To achieve these goals, we convert the coupled system of Atangana–Baleanu fractional equations into an integral equation form with the help of Green functions. The existence of the solution is proven by using topological degree theory and Banach’s fixed point theorem, with which we analyze the solution’s continuity, equicontinuity and boundedness. Then, we use Arzela–Ascolli theory to ensure that the solution is completely continuous. Uniqueness is established using the Banach contraction principle. We also investigate several adequate conditions for HU-stability and generalized HU-stability of the solution. An illustrative example is presented to verify our results.