EXISTENCE OF THREE POSITIVE SOLUTIONS FOR A CLASS OF RIEMANN-LIOUVILLE FRACTIONAL <i>Q</i>-DIFFERENCE EQUATION

Shugui Kang; Huiqin Chen; Luping Li; Yaqiong Cui; Shiwang Ma

doi:10.11948/2156-907X.20180118

2019 Volume 9 Issue 2

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Shugui Kang, Huiqin Chen, Luping Li, Yaqiong Cui, Shiwang Ma. EXISTENCE OF THREE POSITIVE SOLUTIONS FOR A CLASS OF RIEMANN-LIOUVILLE FRACTIONAL Q-DIFFERENCE EQUATION[J]. Journal of Applied Analysis & Computation, 2019, 9(2): 590-600. doi: 10.11948/2156-907X.20180118

Citation:

Shugui Kang, Huiqin Chen, Luping Li, Yaqiong Cui, Shiwang Ma. EXISTENCE OF THREE POSITIVE SOLUTIONS FOR A CLASS OF RIEMANN-LIOUVILLE FRACTIONAL Q-DIFFERENCE EQUATION[J]. Journal of Applied Analysis & Computation, 2019, 9(2): 590-600. doi: 10.11948/2156-907X.20180118

EXISTENCE OF THREE POSITIVE SOLUTIONS FOR A CLASS OF RIEMANN-LIOUVILLE FRACTIONAL Q-DIFFERENCE EQUATION

1.
School of Mathematics and Statistics, Shanxi Datong University, Xingyun Street, 037009, China
2.
School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China

Corresponding author: Email address:dtkangshugui@126.com(S. Kang)
Fund Project: The authors were supported by National Natural Science Foundation of China (Grant No.11871314), Shanxi Datong Scientific Research Project(2018146), Scientific Research Project of Shanxi Datong University(2016K9, 2017K4) and 131 Talent Project at Shanxi Province

Abstract

Abstract

In this paper, we confirm the existence of three positive solutions for a class of Riemann-Liouville fractional $q$-difference equation which satisfies the boundary conditions. We gain several sufficient conditions for the existence of three positive solutions of this boundary value problem by applying the Leggett-Williams fixed point theorem.
- Fractional $q$-integral of the Riemann-Liouville /
- fractional $q$-derivative of the Riemann-Liouville /
- fixed point theorem /
- fractional $q$-difference equation /
- positive solutions
MSC: 39A13, 34A08, 34B18

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