Generalized UH-stability of a nonlinear fractional coupling $(\mathcalligra{p}_{1},\mathcalligra{p}_{2})$-Laplacian system concerned with nonsingular Atangana–Baleanu fractional calculus
Kaihong Zhao
Abstract
Abstract The classical $\mathcalligra{p}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> </mml:math> -Laplace equation is one of the special and significant second-order ODEs. The fractional-order $\mathcalligra{p}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> </mml:math> -Laplace ODE is an important generalization. In this paper, we mainly treat with a nonlinear coupling $(\mathcalligra{p}_{1},\mathcalligra{p}_{2})$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>p</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>p</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>)</mml:mo> </mml:math> -Laplacian systems involving the nonsingular Atangana–Baleanu (AB) fractional derivative. In accordance with the value range of parameters $\mathcalligra{p}_{1}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>p</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> and $\mathcalligra{p}_{2}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>p</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> , 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.