Existence of solutions of boundary value problems for singular fractional q-difference equations

  • Kuikui Ma
  • Shurong Sun
  • Zhenlai HanEmail author
Original Research


In this paper, we study the existence and uniqueness of solutions for a class of singular three-point boundary value problems of fractional q-difference equations invovling fractional q-derivative of Riemann–Liouville type. Based on the generalization of Banach contraction principle, we obtain a sufficient condition for existence and uniqueness of solutions of the problem. By applying the Krasnoselskii’s fixed point theorem, we establish a sufficient condition for the existence of at least one solution of the problem. As applications, two examples are presented to illustrate our main results.


Fractional q-difference equations Singular nonlinear boundary value problems The fixed point theorem 

Mathematics Subject Classification

34B16 39A13 34A08 47H10 



The authors sincerely thank the reviewers for their valuable suggestions and useful comments that have led to the present improved version of the original manuscript. This research is supported by the Natural Science Foundation of China (11571202, 61374074), and supported by Shandong Provincial Natural Science Foundation (ZR2014AP011, ZR2013AL003).


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Copyright information

© Korean Society for Computational and Applied Mathematics 2016

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of JinanJinanPeople’s Republic of China

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