Abstract and Applied Analysis

Positive Solutions for Boundary Value Problems of Singular Fractional Differential Equations

Zhanbing Bai, Weichen Sun, and Weihai Zhang

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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 + α u + f t , u , D C 0 + ν u , D C 0 + μ u + g t , u , D C 0 + ν u , D C 0 + μ u = 0 , u 0 = u 0 = u 0 = u 0 = 0 , where 3 < α < 4 , 0 < ν < 1 , 1 < μ < 2 , D C 0 + α 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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 129640, 7 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393443526

Digital Object Identifier
doi:10.1155/2013/129640

Mathematical Reviews number (MathSciNet)
MR3064542

Zentralblatt MATH identifier
1307.34005

Citation

Bai, Zhanbing; Sun, Weichen; Zhang, Weihai. Positive Solutions for Boundary Value Problems of Singular Fractional Differential Equations. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 129640, 7 pages. doi:10.1155/2013/129640. https://projecteuclid.org/euclid.aaa/1393443526


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