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Existence and Uniqueness Theorem of the Solution to a Class of Nonlinear Nabla Fractional Difference System with a Time Delay

  • Churong Chen
  • Baoguo Jia
  • Xiang LiuEmail author
  • Lynn Erbe
Article
  • 68 Downloads

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.

Keywords

Discrete fractional calculus existence and uniqueness time delay 

Mathematics Subject Classification

39A12 39A70 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Churong Chen
    • 1
  • Baoguo Jia
    • 2
  • Xiang Liu
    • 1
    Email author
  • Lynn Erbe
    • 3
  1. 1.School of MathematicsSun Yat-Sen UniversityGuangzhouChina
  2. 2.Guangdong Province Key Laboratory of Computational Science School of MathematicsSun Yat-Sen UniversityGuangzhouChina
  3. 3.Department of MathematicsUniversity of Nebraska-LincolnLincolnUSA

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