Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations

Loading...
Thumbnail Image

Date

2011

Journal Title

Journal ISSN

Volume Title

Type

Article

Publisher

ELSEVIER SCIENCE INC

Series Info

APPLIED MATHEMATICAL MODELLING;Volume: 35 Issue: 12 Pages: 5662-5672

Scientific Journal Rankings

Abstract

In this paper, we state and prove a new formula expressing explicitly the derivatives of shifted Chebyshev polynomials of any degree and for any fractional-order in terms of shifted Chebyshev polynomials themselves. We develop also a direct solution technique for solving the linear multi-order fractional differential equations (FDEs) with constant coefficients using a spectral tau method. The spatial approximation with its fractional-order derivatives (described in the Caputo sense) are based on shifted Chebyshev polynomials T(L,n)(x) with x is an element of (0,L), L > 0 and n is the polynomial degree. We presented a shifted Chebyshev collocation method with shifted Chebyshev-Gauss points used as collocation nodes for solving nonlinear multi-order fractional initial value problems. Several numerical examples are considered aiming to demonstrate the validity and applicability of the proposed techniques and to compare with the existing results. (C) 2011 Elsevier Inc. All rights reserved.

Description

Keywords

October University for Multi-term fractional differential equations, Nonlinear fractional differential equations, Tau method, Collocation method, Shifted Chebyshev polynomials, Gauss quadrature

Citation