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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

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

Published: 5 September 2011


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.

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