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Optimal Homotopy Anaylsis Method for Nonlinear Partial Fractional Differential Fisher's Equation

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In this article, we use the fractional complex transform and the optimal homotopy analysis method (OHAM) to find the analytical approximate solutions for time-space nonlinear partial fractional Fisher's equation. Fractional complex transformation is proposed to convert time-space nonlinear partial fractional differential Fisher's equation to nonlinear partial differential equations. Also, we use the OHAM to find the numerical solution for nonlinear PFDEs. This optimal approach has general meaning and can be used to get the fast convergent series solutions of the different type of nonlinear partial fractional differential equations. The results reveal that this method is very effective and powerfull to obtain the approximate solutions. The OHAM contains a certain auxiliary parameter h which provides us a simple way to adjust and control the convergence region to the series solution.
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Keywords: FRACTIONAL CALCULUS; FRACTIONAL COMPLEX TRANSFORM; OPTIMAL HOMOTOPY ANALYSIS METHOD; THE TIME-SPACE FRACTIONAL FISHER'S EQUATION

Document Type: Research Article

Publication date: April 1, 2015

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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