Unique Solutions for Fractional q-Difference Boundary Value Problems Via a Fixed Point Method

  • Jing Ren
  • Chengbo ZhaiEmail author


In this paper, by applying the cone theory in ordered Banach spaces associated with the characters of increasing \(\varphi -(h,e)\)-concave operators, we investigate the existence and uniqueness of nontrivial solutions for a nonlinear fractional q-difference equation boundary value problem. The main results show that we can construct an iterative scheme approximating the unique nontrivial solution. Relying on an example, we show the efficiency and applicability of the main result.


Fractional q-difference equation Existence and uniqueness Nontrivial solution \(\varphi -(h, e)\)-Concave operator 

Mathematics Subject Classification

34B18 33D05 39A13 



This paper was supported financially by the Youth Science Foundation of China (11201272), Shanxi Province Science Foundation (2015011005) and 131 Talents Project of Shanxi Province (2015).


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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesShanxi UniversityTaiyuanPeople’s Republic of China

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