Solvability for fractional order boundary value problems at resonance

In this paper, by using the coincidence degree theory, we consider the following boundary value problem for fractional differential equation D 0 + α x ( t ) = f ( t , x ( t ) , x ′ ( t ) , x ″ ( t ) ) , t ∈ [ 0 , 1 ] , x ( 0 ) = x ( 1 ) , x ′ ( 0 ) = x ″ ( 0 ) = 0 , where D 0 + α 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.