Numerical solutions for fractional differential equations by Tau-Collocation method

Abstract

The main purpose of this paper is to provide an efficient numerical approach for multi-order fractional differential equations based on a Tau-Collocation method. To do this, multi-order fractional differential equations transformed into a system of nonlinear algebraic equations in matrix form. Thus, by solving this system unknown coefficients are obtained. The fractional derivatives are described in the Caputo sense. The rate of convergence for the proposed method is established in the Lwp norm. Some numerical example is also provided to illustrate our results. The results reveal that the method is very effective and simple.