| Summary: | Abstract The classical p $\mathcalligra{p}$ -Laplace equation is one of the special and significant second-order ODEs. The fractional-order p $\mathcalligra{p}$ -Laplace ODE is an important generalization. In this paper, we mainly treat with a nonlinear coupling ( p 1 , p 2 ) $(\mathcalligra{p}_{1},\mathcalligra{p}_{2})$ -Laplacian systems involving the nonsingular Atangana–Baleanu (AB) fractional derivative. In accordance with the value range of parameters p 1 $\mathcalligra{p}_{1}$ and p 2 $\mathcalligra{p}_{2}$ , 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.
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