Solving initial and boundary value problems of fractional ordinary differential equations by using collocation and fractional powers

This paper presents a novel approach for solving initial and boundary-values problems on ordinary fractional differential equations. The strategy considered is based on the use of a suitable truncated series expressed in terms of fractional powers of the independent variable, and a collocation approach. With this strategy accurate numerical approximations can be obtained. The error criterion is based on the concepts of residue and relative error. Two algorithms fitted to the nature (linear or nonlinear) of the considered fractional differential equation are proposed. Finally, some problems illustrating the efficiency of the proposed method are presented.