Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1811-96
Keywords
Nabla $(q, h)$-fractional difference equations, stability, discrete fractional Lyapunov direct method, Lyapunov functions
First Page
664
Last Page
687
Recommended Citation
LIU, X, JIA, B, ERBE, L, & PETERSON, A (2019). Stability analysis for a class of nabla $(q,h)$-fractional difference equations. Turkish Journal of Mathematics 43 (2): 664-687. https://doi.org/10.3906/mat-1811-96
