Legendre Wavelet Operational Matrix of Fractional Derivative through Wavelet-Polynomial Transformation and Its Applications on Non-Linear System of Fractional Order Differential Equations

摘要

In this article we propose the wavelet operational method based on shifted Legendre polynomial to obtain the numerical solutions of non-linear systems of fractional order differential equations (NSFDEs). The operational matrix of fractional derivative derived through wavelet-polynomial transformation are used together with the collocation method to turn the NSFDEs to a system of non-linear algebraic equations. Illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques.