Quintic spline collocation method for fractional boundary value problems

The spline collocation method is a competent and highly effective mathematical tool for constructing the approximate solutions of boundary value problems arising in science, engineering and mathematical physics. In this paper, a quintic polynomial spline collocation method is employed for a class of fractional boundary value problems (FBVPs). The FBVPs are expressed in terms of Caputo's fractional derivative in this approach. The consistency relations are derived in order to compute the approximate solutions of FBVPs. Finally, numerical results are given, which demonstrate the effectiveness of the numerical scheme.