Existence and Uniqueness Theorem of the Solution to a Class of Nonlinear Nabla Fractional Difference System with a Time Delay |
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| Authors: | Churong?Chen Baoguo?Jia Email author" target="_blank">Xiang?LiuEmail author Lynn?Erbe |
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| Institution: | 1.School of Mathematics,Sun Yat-Sen University,Guangzhou,China;2.Guangdong Province Key Laboratory of Computational Science School of Mathematics,Sun Yat-Sen University,Guangzhou,China;3.Department of Mathematics,University of Nebraska-Lincoln,Lincoln,USA |
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| Abstract: | In this paper, we investigate an existence and uniqueness theorem of the solution to a class of nonlinear nabla fractional difference system with a time delay. More precisely, observing \(\nu (t-k)^{\overline{\nu -1}}\le {t^{\bar{\nu }}}\), we get the evaluation of \(\nabla _{a+k}^{-\nu } ||z(t-k)||\), which allows us to apply the generalized Gronwall’s inequality for the solutions of nonlinear nabla fractional difference system. The theorems we establish fill the gaps in some existing papers. |
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