Numerical solutions of fractional partial differential equations by using Legendre wavelets

A numerical method based on Legendre wavelets is proposed for fractional partial differential equations. Legendre wavelets operational matrices of fractional order integration and fractional order differentiation are derived. By using these matrices, each term of the problem was converted into matrix form. Lastly, the equation was transformed into a Sylvester equation. The error estimation of the Legendre wavelets method is given in Theorem 5.1. Three numerical examples are shown to demonstrate the validity and applicability of the method.