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