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A generalized q-fractional Gronwall inequality and its applications to nonlinear delay q-fractional difference systems
Journal article   Open access  Peer reviewed

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

Thabet Abdeljawad, Jehad Alzabut and Dumitru Baleanu
Journal of inequalities and applications, Vol.2016(1), pp.1-13
29/09/2016
DOI: https://doi.org/10.1186/s13660-016-1181-2

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
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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https://doi.org/10.1186/s13660-016-1181-2View
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