Liapunov functional and stability of linear nabla (q, h)-fractional difference equations

Abstract

In this paper we will use a Liapunov functional to prove the stability of the trivial solution of the () order nabla (q, h)-fractional difference equation (0.1) where the operator in this equation is defined in Definition 2.3. When and this fractional difference equation is a fractional nabla quantum difference equation (see the monograph by Kac and Cheung) and when and this fractional equation is simply an order nabla difference equation.