A generalized q -fractional Gronwall inequality and its applications to nonlinear delay q -fractional difference systems

Journal of inequalities and applications

Thabet Abdeljawad¹ 

关键词: generalized q-fractional Gronwall inequality;    delay q-fractional difference system;    uniqueness of solution;    estimate for the solution;    26A33;    39A11;   

DOI  :  10.1186/s13660-016-1181-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we state and prove a new discrete q-fractional version of the Gronwall inequality. Based on this result, a particular version expressed by means of the q-Mittag-Leffler function is provided. To apply the proposed results, we prove the uniqueness and obtain an estimate for the solutions of nonlinear delay Caputo q-fractional difference system. We examine our results by providing a numerical example.

【 授权许可】

CC BY