Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 8 (2013), 35 -- 49

APPROXIMATE ANALYTICAL SOLUTION OF DIFFUSION EQUATION WITH FRACTIONAL TIME DERIVATIVE USING OPTIMAL HOMOTOPY ANALYSIS METHOD

S. Das, K. Vishal and P. K. Gupta

Abstract. In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution. Effects of parameters on the convergence of the approximate series solution by minimizing the averaged residual error with the proper choices of parameters are calculated numerically and presented through graphs and tables for different particular cases.

2010 Mathematics Subject Classification: 26A33; 34A08; 60G22; 65Gxx.
Keywords: Diffusion equation; Caputo derivative; Error analysis; Homotopy analysis method.

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S. Das K. Vishal
Department of Applied Mathematics, Department of Applied Mathematics,
Indian Institute of Technology, Indian Institute of Technology,
Banaras Hindu University, Banaras Hindu University,
Varanasi - 221 005, India. Varanasi - 221 005, India.
e-mail: subir_das08@hotmail.com
P. K. Gupta
Indian Institute of Technology,
Banaras Hindu University,
Varanasi - 221 005, India.

http://www.utgjiu.ro/math/sma