EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR NONLINEAR FRACTIONAL <i>Q</i>-DIFFERENCE EQUATION WITH INTEGRAL BOUNDARY CONDITIONS

Caixia Guo; Jianmin Guo; Shugui Kang; Huapeng Li

doi:10.11948/20190055

2020 Volume 10 Issue 1

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Caixia Guo, Jianmin Guo, Shugui Kang, Huapeng Li. EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR NONLINEAR FRACTIONAL Q-DIFFERENCE EQUATION WITH INTEGRAL BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 153-164. doi: 10.11948/20190055

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Caixia Guo, Jianmin Guo, Shugui Kang, Huapeng Li. EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR NONLINEAR FRACTIONAL Q-DIFFERENCE EQUATION WITH INTEGRAL BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 153-164. doi: 10.11948/20190055

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR NONLINEAR FRACTIONAL Q-DIFFERENCE EQUATION WITH INTEGRAL BOUNDARY CONDITIONS

1.
School of Mathematics and Statistics, Shanxi Datong University, Xingyun Street, 037009, China

Corresponding author: Email address: lihuaa1_0@163.com(H. Li)
Fund Project: The authors were supported by National Natural Science Foundation of China (Nos.11871314, 61803241), Applied Foundational Research Project of the Datong Science and Technology Bureau(2019154) and 131 Talent Project at Shanxi Province

Abstract

Abstract

This paper studies a class of nonlinear fractional $q$-difference equations with integral boundary conditions. By exploiting the properties of Green's function and two fixed point theorems for a sum operator, the existence and uniqueness of positive solutions for the boundary value problem are established. Iterative schemes for approximating the solutions are also obtained. Explicit examples are given to illustrate main results.
- Fractional $q$-difference /
- integral boundary value problem /
- fixed point theorem /
- positive solution
MSC: 34A08, 34K30

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References

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