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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This work is supported by the National Natural Science Foundation of China (no. 11271380), Guangdong Province Key Laboratory of Computational Science, and the International Program for Ph.D. Candidates, Sun Yat-Sen University.
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Chen, C., Jia, B., Liu, X. et al. Existence and Uniqueness Theorem of the Solution to a Class of Nonlinear Nabla Fractional Difference System with a Time Delay. Mediterr. J. Math. 15, 212 (2018). https://doi.org/10.1007/s00009-018-1258-x
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DOI: https://doi.org/10.1007/s00009-018-1258-x