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

Abdeljawad, ThabetAlzabut, JehadBaleanu, Dumitru2018-09-262018-09-262016Abdeljawad, T., Alzabut, J., Baleanu, D. (2016). A generalized q-fractional Gronwall inequality and its applications to nonlinear delay q-fractional difference systems. Journal Of Inequalities Applications. http://dx.doi.org/ 10.1186/s13660-016-1181-21029-242Xhttp://hdl.handle.net/20.500.12416/1796In 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.eninfo:eu-repo/semantics/openAccessGeneralized Q-Fractional Gronwall InequalityDelay Q-Fractional Difference SystemUniqueness Of SolutionEstimate For The SolutionA generalized q-fractional Gronwall inequality and its applications to nonlinear delay q-fractional difference systemsA Generalized Q-Fractional Gronwall Inequality and Its Applications To Nonlinear Delay Q-Fractional Difference SystemsArticle10.1186/s13660-016-1181-2