Finite-time stability and uniqueness theorem of solutions of nabla fractional (q,h)-difference equations with non-Lipschitz and nonlinear conditions

Abstract

In this paper, the discrete $ (q, h) $-fractional Bihari inequality is generalized. On the grounds of inequality, the finite-time stability and uniqueness theorem of solutions of $ (q, h) $-fractional difference equations with non-Lipschitz and nonlinear conditions is concluded. In addition, the validity of our conclusion is illustrated by a nonlinear example with a non-Lipschitz condition.

Keywords

• fractional (q，h)-difference equation
• finite-time stability
• uniqueness
• non-lipschitz condition
• discrete (q，h)-fractional bihari inequality