Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations

Abstract EN

We present a new numerical method to get the approximate solutions of fractional differential equations.

A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived.

Then a modified variational iteration formula which can avoid “noise terms” is constructed.

Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs).

Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms.

Five examples are discussed to demonstrate the validity and applicability of the technique.