- Turkish Journal of Mathematics
- Vol: 43 Issue: 2
- Stability analysis for a class of nabla $(q,h)$-fractional difference equations
Stability analysis for a class of nabla $(q,h)$-fractional difference equations
Authors : Xiang Liu, Baoguo Jia, Lynn Erbe, Allan Peterson
Pages : 664-687
View : 10 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :This paper investigates stability of the nabla $(q,h)$-fractional difference equations. Asymptotic stability of the special nabla $(q,h)$-fractional difference equations are discussed. Stability theorems for discrete fractional Lyapunov direct method are proved. Furthermore, we give some new lemmas (including important comparison theorems) related to the nabla $(q,h)$-fractional difference operators that allow proving the stability of the nabla $(q,h)$-fractional difference equations, by means of the discrete fractional Lyapunov direct method, using Lyapunov functions. Some examples are given to illustrate these results.Keywords : Nabla $(q, h)$-fractional difference equations, stability, discrete fractional Lyapunov direct method, Lyapunov functions