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A Hybrid Technique for Space-Time Fractional Parabolic Differential Equations |
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PP: 545-555 |
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doi:10.18576/pfda/100403
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Author(s) |
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Nasser H. Sweilam,
Waleed Abdel Kareem,
Muner M. Abou Hasan,
Taha H. El-Ghareeb,
Toba M. Soliman,
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Abstract |
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| The main objective of the present article is to present an accurate efficient technique for approximating the solutions of the diffusion equation of fractional space-time Le ́vy-Feller type. The suggested method depends on spectral collocation algorithm and implicit non standard finite difference method. The fractional space-time Le ́vy-Feller diffusion equations are acquired by updating the classical diffusion equations such that the time derivative of the first order will be the fractional Caputo operator and the second-order space derivative will modify to be the Riesz-Feller derivative. The utilized spectral method uses the well known Legendre orthogonal polynomials and the Gauss-Lobatto Chebyshev collocation points. The method depends basically on conversion these kinds of fractional differential equations into a system of algebraic equations which may be solved easily using appropriate technique. The numerical outcomes are presented in the form of tables and graphs to emphasize the reliability of the introduced technique to approximate the solutions of the fractional space-time-Le ́vy-Feller diffusion equations.
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