Solvability for fractional order boundary value problems at resonance

Abstract

In this paper, by using the coincidence degree theory, we consider the following boundary value problem for fractional differential equation {D 0+αx(t) =f(t,x(t),x′(t),x″(t) ), t ε [0,1], {x(0) = x(1), x″(0)=x″(0) = 0, where D α0 denotes the Caputo fractional differential operator of order α, 2 < ≤ 3. A new result on the existence of solutions for above fractional boundary value problem is obtained. © 2011 Hu and Liu licensee Springer.