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Existence and asymptotic analysis of positive solutions for a singular fractional differential equation with nonlocal boundary conditions

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Authors
He, J.
Zhang, Xinguang
Liu, Lishan
Wu, Yong Hong
Cui, Y.
Date
2018
Type
Journal Article

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He, J. and Zhang, X. and Liu, L. and Wu, Y.H. and Cui, Y. 2018. Existence and asymptotic analysis of positive solutions for a singular fractional differential equation with nonlocal boundary conditions. Boundary Value Problems. 2018 (1): Article ID 189.
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Boundary Value Problems
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School of Electrical Engineering, Computing and Mathematical Science (EECMS)
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Abstract

In this paper, we focus on the existence and asymptotic analysis of positive solutions for a class of singular fractional differential equations subject to nonlocal boundary conditions. By constructing suitable upper and lower solutions and employing Schauder’s fixed point theorem, the conditions for the existence of positive solutions are established and the asymptotic analysis for the obtained solution is carried out. In our work, the nonlinear function involved in the equation not only contains fractional derivatives of unknown functions but also has a stronger singularity at some points of the time and space variables.

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