A new Jacobi operational matrix: An application for solving fractional differential equations

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• 作者：E.H. Doha^a ; ^{eiddoha@frcu.eun.eg} ; A.H. Bhrawy^b ; ^{alibhrawy@yahoo.co.uk} ; S.S. Ezz-Eldien^c ; ^{s_sezeldien@yahoo.com}
• 关键词：Multi-term fractional differential equations ; Nonlinear fractional differential equations ; Operational matrix ; Jacobi polynomials ; Spectral method ; Caputo derivative
• 刊名：Applied Mathematical Modelling
• 出版年：2012
• 期刊代码：6_0307904x
• 类别：cp
• 出版时间：October, 2012
• 卷：36
• 期：10
• 页码：4931-4943
• 文件大小：295 K

摘要

In this paper, we derived the shifted Jacobi operational matrix (JOM) of fractional derivatives which is applied together with spectral tau method for numerical solution of general linear multi-term fractional differential equations (FDEs). A new approach implementing shifted Jacobi operational matrix in combination with the shifted Jacobi collocation technique is introduced for the numerical solution of nonlinear multi-term FDEs. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifying the problem. The proposed methods are applied for solving linear and nonlinear multi-term FDEs subject to initial or boundary conditions, and the exact solutions are obtained for some tested problems. Special attention is given to the comparison of the numerical results obtained by the new algorithm with those found by other known methods.