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Numerical solution of fractional differential equations with a collocation method based on Müntz polynomials. (English) Zbl 1228.65132
Summary: This paper presents a computational technique based on the collocation method and Müntz polynomials for the solution of fractional differential equations. An appropriate representation of the solution via the Müntz 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.

MSC:
65L70 Error bounds for numerical methods for ordinary differential equations
34A08 Fractional ordinary differential equations and fractional differential inclusions
26A33 Fractional derivatives and integrals
45J05 Integro-ordinary differential equations
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