Existence of positive solution for a fractional order nonlinear differential system involving a changing sign perturbation

Volume 9, Issue 5, pp 2076--2085 http://dx.doi.org/10.22436/jnsa.009.05.13

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Authors

Jianxin He - School of Science, Nanjing University of Science and Technology, Nanjing, 210094, P. R. China. - School of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, P. R. China. Xinguang Zhang - School of Mathematical and Informational Sciences, Yantai University, Yantai 264005, Shandong, China. - Department of Mathematics and Statistics, Curtin University of Technology, WA 6845, Perth, Australia. Yonghong Wu - Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia.

Abstract

In this paper, we study a class of singular fractional order differential system with a changing-sign perturbation which arises from uid dynamics, biological models, electrical networks with uncertain physical parameters and parametrical variations in time. Under suitable growth condition, the singular changing- sign system is transformed to an approximately singular fractional order differential system with positive nonlinear term, then the existence of positive solution is established by using the known fixed point theorem.

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Keywords

• Singular phenomena
• changing-sign perturbation
• positive solution
• Riemann-Stieltjes integral conditions.

MSC

•  34B15
•  34B18

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