SUCCESSIVE ITERATIONS FOR UNIQUE POSITIVE SOLUTION OF A NONLINEAR FRACTIONAL Q-INTEGRAL BOUNDARY VALUE PROBLEM

Guotao Wang; Zhanbing Bai; Lihong Zhang

doi:10.11948/2156-907X.20180193

2019 Volume 9 Issue 4

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Guotao Wang, Zhanbing Bai, Lihong Zhang. SUCCESSIVE ITERATIONS FOR UNIQUE POSITIVE SOLUTION OF A NONLINEAR FRACTIONAL Q-INTEGRAL BOUNDARY VALUE PROBLEM[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1204-1215. doi: 10.11948/2156-907X.20180193

Citation:

Guotao Wang, Zhanbing Bai, Lihong Zhang. SUCCESSIVE ITERATIONS FOR UNIQUE POSITIVE SOLUTION OF A NONLINEAR FRACTIONAL Q-INTEGRAL BOUNDARY VALUE PROBLEM[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1204-1215. doi: 10.11948/2156-907X.20180193

SUCCESSIVE ITERATIONS FOR UNIQUE POSITIVE SOLUTION OF A NONLINEAR FRACTIONAL Q-INTEGRAL BOUNDARY VALUE PROBLEM

1.
School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, China
2.
College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, China
3.
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Corresponding author: Email address:zhanglih149@126.com(L. Zhang)
Fund Project: Partially supported by National Natural Science Foundation of China(Nos. 11501342 and 11571207), the Natural Science Foundation for Young Scientists of Shanxi Province, China(No. 201701D221007) and STIP(Nos. 201802068 and 201802069)

Abstract

Abstract

In this paper, under certain nonlinear growth conditions, we investigate the existence and successive iterations for the unique positive solution of a nonlinear fractional $ q $-integral boundary problem by employing hybrid monotone method, which is a novel approach to nonlinear fractional $ q $-difference equation. This paper not only proves the existence of the unique positive solution, but also gives some computable explicit hybrid iterative sequences approximating to the unique positive solution.
- Fractional q-difference equation /
- q-integral condition /
- explicit iterative sequence /
- hybrid monotone method.
MSC: 34A08, 34B10, 34B18, 39A10

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References

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