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2013 Positive Solutions for Boundary Value Problems of Singular Fractional Differential Equations
Zhanbing Bai, Weichen Sun, Weihai Zhang
Abstr. Appl. Anal. 2013(SI42): 1-7 (2013). DOI: 10.1155/2013/129640

Abstract

In this paper, by using a fixed point theorem, we investigate the existence of a positive solution to the singular fractional boundary value problem ${D_{C}}_{0+}^{\alpha }u+f(t,u,{D_{C}}_{0+}^{\nu }u,{D_{C}}_{0+}^{\mu }u)+g(t,u,{D_{C}}_{0+}^{\nu }u,{D_{C}}_{0+}^{\mu }u)=0$, $u(0)={u}^{\prime }(0)={u}^{\prime \prime }(0)={u}^{\prime \prime \prime }(0)=0$, where $3<\alpha <4$, $0<\nu <1$, $1<\mu <2$, ${D_{C}}_{0+}^{\alpha }$ is Caputo fractional derivative, $f(t,x,y,z)$ is singular at the value 0 of its arguments $x,y,z$, and $g(t,x,y,z)$ satisfies the Lipschitz condition.

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Zhanbing Bai. Weichen Sun. Weihai Zhang. "Positive Solutions for Boundary Value Problems of Singular Fractional Differential Equations." Abstr. Appl. Anal. 2013 (SI42) 1 - 7, 2013. https://doi.org/10.1155/2013/129640

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1307.34005
MathSciNet: MR3064542
Digital Object Identifier: 10.1155/2013/129640

Rights: Copyright © 2013 Hindawi

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