Stability analysis by fixed point theorems for a class of non-linear Caputo nabla fractional difference equation

Advances in Difference Equations

article

Butt, Rabia Ilyas¹  Abdeljawad, Thabet²  ur Rehman, Mujeeb¹ 

[1] Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology;Department of Mathematics and General Sciences, Prince Sultan University;Department of Medical Research, China Medical University;Department of Computer Science and Information Engineering, Asia University

关键词: Caputo nabla fractional difference;    Stability;    Schauder’s fixed point theorem;    Banach contraction principle;    Krasnoselskii’s fixed point theorem;   

DOI  :  10.1186/s13662-020-02674-1

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

Fractional difference equations have become important due to their qualitative properties and applications in discrete modeling. Stability analysis of solutions is one of the most widely used qualitative properties with tremendous applications. In this paper, we investigate the existence and stability results for a class of non-linear Caputo nabla fractional difference equations. To obtain the existence and stability results, we use Schauder’s fixed point theorem, the Banach contraction principle and Krasnoselskii’s fixed point theorem. The analysis of the theoretical results depends on the structure of nabla discrete Mittag-Leffler functions. An example is provided to illustrate the theoretical results.

【 授权许可】

CC BY