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, XIANG; JIA, BAOGUO; ERBE, LYNN; and PETERSON, ALLAN
(2019)
"Stability analysis for a class of nabla $(q,h)$-fractional difference equations,"
Turkish Journal of Mathematics: Vol. 43:
No.
2, Article 8.
https://doi.org/10.3906/mat-1811-96
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss2/8
