The operational matrix formulation of the Jacobi tau approximation for space fractional diffusion equation

被引：0
作者：
Eid H Doha
Ali H Bhrawy
Dumitru Baleanu
Samer S Ezz-Eldien
机构：
[1] Cairo University,Department of Mathematics, Faculty of Science
[2] King Abdulaziz University,Department of Mathematics, Faculty of Science
[3] Beni-Suef University,Department of Mathematics, Faculty of Science
[4] King Abdulaziz University,Department of Chemical and Materials Engineering, Faculty of Engineering
[5] Cankaya University,Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences
[6] Institute of Space Sciences,Department of Basic Science
[7] Institute of Information Technology,undefined
[8] Modern Academy,undefined
来源：
Advances in Difference Equations | / 2014卷
关键词：
multi-term fractional differential equations; fractional diffusion equations; tau method; shifted Jacobi polynomials; operational matrix; Caputo derivative;
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摘要：
In this article, an accurate and efficient numerical method is presented for solving the space-fractional order diffusion equation (SFDE). Jacobi polynomials are used to approximate the solution of the equation as a base of the tau spectral method which is based on the Jacobi operational matrices of fractional derivative and integration. The main advantage of this method is based upon reducing the nonlinear partial differential equation into a system of algebraic equations in the expansion coefficient of the solution. In order to test the accuracy and efficiency of our method, the solutions of the examples presented are introduced in the form of tables to make a comparison with those obtained by other methods and with the exact solutions easy.
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  • [1] Su L(2010)Finite difference methods for fractional dispersion equations Appl. Math. Comput 216 3329-3334
  • [2] Wang W(2010)Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations Appl. Math. Comput 216 2276-2285
  • [3] Xu Q(2009)Homotopy analysis method for fractional IVPs Commun. Nonlinear Sci. Numer. Simul 14 674-684
  • [4] Li YL(2010)A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations Appl. Math. Model 34 593-600
  • [5] Hashim I(2011)Application of Legendre wavelets for solving fractional differential equations Comput. Math. Appl 62 1038-1045
  • [6] Abdulaziz O(2008)Application of homotopy-perturbation method to fractional IVPs J. Comput. Appl. Math 216 574-584
  • [7] Momani S(2008)Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order Chaos Solitons Fractals 36 167-174
  • [8] Odibat Z(2010)Convergence of the variational iteration method for solving multi-order fractional differential equations Comput. Math. Appl 60 2871-2879
  • [9] Momani S(2011)Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations Appl. Math. Model 35 5662-5672
  • [10] Xu H(2011)A quadrature tau method for variable coefficients fractional differential equations Appl. Math. Lett 24 2146-2152
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