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

作者：Abdeljawad Thabet^*; Alzabut Jehad; Baleanu Dumitru

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016, 2016(1): 240.

DOI：10.1186/s13660-016-1181-2

• generalized q-fractional Gronwall inequality
• delay q-fractional difference system
• uniqueness of solution
• estimate for the solution

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.

• 出版日期2016-9-29