Generalized UH-stability of a nonlinear fractional coupling (mathcalligra{p}_{1},mathcalligra{p}_{2})-Laplacian system concerned with nonsingular Atangana–Baleanu fractional calculus

Abstract

The classical mathcalligra{p}-Laplace equation is one of the special and significant second-order ODEs. The fractional-order mathcalligra{p}-Laplace ODE is an important generalization. In this paper, we mainly treat with a nonlinear coupling (mathcalligra{p}_{1},mathcalligra{p}_{2})-Laplacian systems involving the nonsingular Atangana–Baleanu (AB) fractional derivative. In accordance with the value range of parameters mathcalligra{p}_{1} and mathcalligra{p}_{2}, we obtain sufficient criteria for the existence and uniqueness of solution in four cases. By using some inequality techniques we further establish the generalized UH-stability for this system. Finally, we test the validity and practicality of the main results by an example.