On Shifted Jacobi Spectral Approximations For Solving Fractional Differential Equations
No Thumbnail Available
Date
2013
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier Science
Open Access Color
OpenAIRE Downloads
OpenAIRE Views
Abstract
In this paper, a new formula of Caputo fractional-order derivatives of shifted Jacobi polynomials of any degree in terms of shifted Jacobi polynomials themselves is proved. We discuss a direct solution technique for linear multi-order fractional differential equations (FDEs) subject to nonhomogeneous initial conditions using a shifted Jacobi tau approximation. A quadrature shifted Jacobi tau (Q-SJT) approximation is introduced for the solution of linear multi-order FDEs with variable coefficients. We also propose a shifted Jacobi collocation technique for solving nonlinear multi-order fractional initial value. problems. The advantages of using the proposed techniques are discussed and we compare them with other existing methods. We investigate some illustrative examples of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques. (C) 2013 Elsevier Inc. All rights reserved.
Description
Keywords
Multi-Term Fractional Differential Equations, Nonlinear Fractional Initial Value Problems, Spectral Methods, Shifted Jacobi Polynomials, Jacobi-Gauss-Lobatto Quadrature, Caputo Derivative
Turkish CoHE Thesis Center URL
Fields of Science
Citation
WoS Q
Scopus Q
Source
Applied Mathematics and Computation
Volume
219
Issue
15
Start Page
8042
End Page
8056