Journal
JOURNAL OF INEQUALITIES AND APPLICATIONS
Volume -, Issue -, Pages -Publisher
SPRINGEROPEN
DOI: 10.1186/s13660-016-1181-2
Keywords
generalized q-fractional Gronwall inequality; delay q-fractional difference system; uniqueness of solution; estimate for the solution
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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.
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