EXISTENCE OF POSITIVE SOLUTIONS TO A BOUNDARY VALUE PROBLEM FOR A DELAYED SINGULAR HIGH ORDER FRACTIONAL DIFFERENTIAL EQUATION WITH SIGN-CHANGING NONLINEARITY

Dongyue Liu; Kemei Zhang

doi:10.11948/20190190

2020 Volume 10 Issue 3

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Dongyue Liu, Kemei Zhang. EXISTENCE OF POSITIVE SOLUTIONS TO A BOUNDARY VALUE PROBLEM FOR A DELAYED SINGULAR HIGH ORDER FRACTIONAL DIFFERENTIAL EQUATION WITH SIGN-CHANGING NONLINEARITY[J]. Journal of Applied Analysis & Computation, 2020, 10(3): 1073-1093. doi: 10.11948/20190190

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Dongyue Liu, Kemei Zhang. EXISTENCE OF POSITIVE SOLUTIONS TO A BOUNDARY VALUE PROBLEM FOR A DELAYED SINGULAR HIGH ORDER FRACTIONAL DIFFERENTIAL EQUATION WITH SIGN-CHANGING NONLINEARITY[J]. Journal of Applied Analysis & Computation, 2020, 10(3): 1073-1093. doi: 10.11948/20190190

EXISTENCE OF POSITIVE SOLUTIONS TO A BOUNDARY VALUE PROBLEM FOR A DELAYED SINGULAR HIGH ORDER FRACTIONAL DIFFERENTIAL EQUATION WITH SIGN-CHANGING NONLINEARITY

Dongyue Liu¹,
Kemei Zhang^1, ,

1.
School of Mathematical Sciences, Qufu Normal University, No.57 Jingxuan West Road, Qufu, Shandong 273165, China

Corresponding author: Email address:zhkm90@126.com(K. Zhang)
Fund Project: The authors were supported by National Natural Science Foundation of China (No. 11571197) and National Science Foundation of Shandong (No. ZR2016FM10)

Abstract

Abstract

In this paper, we discuss the existence of positive solutions to the boundary value problem for a high order fractional differential equation with delay and singularities including changing sign nonlinearity. By using the properties of the Green function, Guo-krasnosel'skii fixed point theorem, Leray-Schauder's nonlinear alternative theorem, some existence results of positive solutions are obtained, respectively.
- Positive solution /
- fractional differential equation /
- delay /
- cone expansion and cone compression fixed point theorem /
- changing sign nonlinearity
MSC: 26A33, 34K10

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References

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