Stability analysis for a class of nabla (q; h)-fractional difference equations | Zendy

Xiang Liu | Zendy; Baoguo Jia | Zendy; Lynn Erbe | Zendy; Allan Peterson | Zendy

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Stability analysis for a class of nabla (q; h)-fractional difference equations

Author(s) -

Xiang Liu,

Baoguo Jia,

Lynn Erbe,

Allan Peterson

Publication year - 2019

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1811-96

Subject(s) - nabla symbol , mathematics , fractional calculus , stability (learning theory) , lyapunov function , pure mathematics , mathematical analysis , nonlinear system , physics , quantum mechanics , machine learning , computer science , omega

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.

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