The Legendre wavelet method for solving fractional differential equations

► We solve fractional differential equations by wavelets. ► An operational matrix is derived. ► Initial and boundary value problems are solved. Fractional differential equations are solved using the Legendre wavelets. An operational matrix of fractional order integration is derived and is utilized to reduce the fractional differential equations to system of algebraic equations. The illustrative examples are provided to demonstrate the applicability, simplicity of the numerical scheme based on the Legendre.