Mathematical Methods in the Applied Sciences, ( ISI ), Year (2014-6) , Pages (1-12)

Title : ( Gegenbauer spectral method for time-fractional convection–diffusion equations with variable coefficients )

Authors: Mohammad Mahdi Izadkhah , Jafar Saberi- Nadjafi ,
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Abstract

In this paper, we study the numerical solution to time-fractional partial differential equations with variable coefficients that involve temporal Caputo derivative. A spectral method based on Gegenbauer polynomials is taken for approximating the solution of the given time-fractional partial differential equation in time and a collocation method in space. The suggested method reduces this type of equation to the solution of a linear algebraic system. Finally, some numerical examples are presented to illustrate the efficiency and accuracy of the proposed method.

Keywords

, Riemann-Liouville fractional derivative, Caputo's fractional derivative, time fractional convection-diffusion equation, time fractional Fokker-Planck equation, 2D Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivatives, Gegenbauer polynomials, Pseudospectral m