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Open Access Research

Existence results of positive solutions for boundary value problems of fractional differential equations

Guoqing Chai

Author Affiliations

College of Mathematics and Statistics, Hubei Normal University, Hubei, 435002, P.R. China

Boundary Value Problems 2013, 2013:109  doi:10.1186/1687-2770-2013-109

Published: 29 April 2013

Abstract

In this paper, we are concerned with the following fractional equation:

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/109/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/109/mathml/M1">View MathML</a>

with the boundary value conditions

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/109/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/109/mathml/M2">View MathML</a>

where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/109/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/109/mathml/M3">View MathML</a> is the standard Caputo derivative with <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/109/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/109/mathml/M4">View MathML</a> and δ, γ are constants with <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/109/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/109/mathml/M5">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/109/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/109/mathml/M6">View MathML</a>. By applying a new fixed point theorem on cone and Krasnoselskii’s fixed point theorem, some existence results of positive solution are obtained.

MSC: 34A08, 34B15, 34B18.

Keywords:
fractional differential equations; existence results; fixed point theorem; positive solution