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Existence of the solutions for a class of nonlinear fractional order three-point boundary value problems with resonance

Zigen Ouyang* and Gangzhao Li

Author Affiliations

School of Mathematics and Physics, School of Nuclear Science and Technology, University of South China, Hengyang, 421001, P.R. China

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Boundary Value Problems 2012, 2012:68  doi:10.1186/1687-2770-2012-68

Published: 1 July 2012

Abstract

A class of nonlinear fractional order differential equation

is investigated in this paper, where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/68/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/68/mathml/M2">View MathML</a> is the standard Riemann-Liouville fractional derivative of order <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/68/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/68/mathml/M3">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/68/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/68/mathml/M4">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/68/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/68/mathml/M5">View MathML</a>. Using intermediate value theorem, we obtain a sufficient condition for the existence of the solutions for the above fractional order differential equations.