Wavelet Collocation Method for Solving Multiorder Fractional Differential Equations

Abstract EN

The operational matrices of fractional-order integration for the Legendreand Chebyshev wavelets are derived.

Block pulse functions and collocation methodare employed to derive a general procedure for forming these matrices for both the Legendreand the Chebyshev wavelets.

Then numerical methods based on wavelet expansionand these operational matrices are proposed.

In this proposed method, by a change ofvariables, the multiorder fractional differential equations (MOFDEs) with nonhomogeneousinitial conditions are transformed to the MOFDEs with homogeneous initialconditions to obtain suitable numerical solution of these problems.

Numerical examplesare provided to demonstrate the applicability and simplicity of the numericalscheme based on the Legendre and Chebyshev wavelets.