Turkish Journal of Mathematics
DOI
10.3906/mat-1811-96
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.
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
