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Existence and uniqueness of positive solution to singular fractional differential equations

Yongqing Wang1*, Lishan Liu12 and Yonghong Wu2

Author Affiliations

1 School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, 273165, People’s Republic of China

2 Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA, 6845, Australia

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Boundary Value Problems 2012, 2012:81  doi:10.1186/1687-2770-2012-81

Published: 28 July 2012

Abstract

In this paper, we discuss the existence and uniqueness of a positive solution to the following singular fractional differential equation with nonlocal boundary value conditions:

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/81/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/81/mathml/M1">View MathML</a>

where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/81/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/81/mathml/M2">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/81/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/81/mathml/M3">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/81/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/81/mathml/M4">View MathML</a> with <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/81/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/81/mathml/M5">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/81/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/81/mathml/M6">View MathML</a> is the standard Riemann-Liouville derivative, f may be singular at <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/81/mathml/M7','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/81/mathml/M7">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/81/mathml/M8','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/81/mathml/M8">View MathML</a>, and <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/81/mathml/M9','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/81/mathml/M9">View MathML</a>.

MSC: 34B10, 34B15.

Keywords:
fractional differential equation; positive solution; iterative scheme; singular boundary value problem