SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Research

Solvability for fractional order boundary value problems at resonance

Zhigang Hu* and Wenbin Liu

Author affiliations

Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, People's Republic of China

For all author emails, please log on.

Citation and License

Boundary Value Problems 2011, 2011:20  doi:10.1186/1687-2770-2011-20

Published: 5 September 2011

Abstract

In this paper, by using the coincidence degree theory, we consider the following boundary value problem for fractional differential equation

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2011/1/20/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2011/1/20/mathml/M1">View MathML</a>

where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2011/1/20/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2011/1/20/mathml/M2">View MathML</a> denotes the Caputo fractional differential operator of order α, 2 < α ≤ 3. A new result on the existence of solutions for above fractional boundary value problem is obtained.

Mathematics Subject Classification (2000): 34A08, 34B15.

Keywords:
Fractional differential equations; boundary value problems; resonance; coincidence degree theory