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Z. Naturforsch. 67a, 203 – 209
(2012)
doi:10.5560/ZNA.2012-0008
Solution of the Nonlinear Fractional Diffusion Equation with Absorbent Term and External Force Using Optimal Homotopy-Analysis Method
1 Department of Applied Mathematics, Institute of Technology, Banaras Hindu University, Varanasi 221005, India
2 Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia
Received September 7, 2011 / revised November 18, 2011 / published online April 2, 2012
Reprint requests to: S. D.; E-mail:
sdas.apm@itbhu.ac.in
In this article, the optimal homotopy-analysis method (HAM) is used to obtain approximate analytic solutions of the time-fractional nonlinear diffusion equation in the presence of an external force and an absorbent term. The fractional derivatives are considered in the Caputo sense to avoid nonzero derivative of constants. Unlike usual HAM this method contains at the most three convergence control parameters which determine the fast convergence of the solution through different choices of convergence control parameters. Effects of proper choice of parameters on the convergence of the approximate series solution by minimizing the averaged residual error for different particular cases are depicted through tables and graphs.
Key words: Fractional Diffusion Equation; Nonlinearity; Optimal Homotopy-Analysis Method; Fractional Brownian Motion; Absorbent Term; Error Analysis.
Mathematics Subject Classification 2000: 26A33; 34G20; 35A20; 35R11; 65Mxx