Numerical solution of fractional differential equations with a collocation method based on Miintz polynomials

摘要

This paper presents a computational technique based on the collocation method and Miintz polynomials for the solution of fractional differential equations. An appropriate representation of the solution via the Muentz polynomials reduces its numerical treatment to the solution of a system of algebraic equations. The main advantage of the present method is its superior accuracy and exponential convergence. Consequently, one can obtain good results even by using a small number of collocation points. The accuracy and performance of the proposed method are examined by means of some numerical experiments.