New Analytical Solutions for Time-Fractional Kolmogorov-Petrovsky-Piskunov Equation with Variety of Initial Boundary Conditions

Thanon Korkiatsakul, Sanoe Koonprasert and Khomsan Neamprem
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Thanon Korkiatsakul: Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Sanoe Koonprasert: Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Khomsan Neamprem: Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand

Mathematics, 2019, vol. 7, issue 9, 1-20

Abstract: The generalized time fractional Kolmogorov-Petrovsky-Piskunov equation (FKPP), D t α ω ( x , t ) = a ( x , t ) D x x ω ( x , t ) + F ( ω ( x , t ) ) , which plays an important role in engineering, chemical reaction problem is proposed by Caputo fractional order derivative sense. In this paper, we develop a framework wavelet, including shift Chebyshev polynomial of the first kind as a mother wavelet, and also construct some operational matrices that represent Caputo fractional derivative to obtain analytical solutions for FKPP equation with three different types of Initial Boundary conditions (Dirichlet, Dirichlet-Neumann, and Neumann-Robin). Our results shown that the Chebyshev wavelet is a powerful method, due to its simplicity, efficiency in analytical approximations, and its fast convergence. The comparison of the Chebyshev wavelet results indicates that the proposed method not only gives satisfactory results but also do not need large amount of CPU times.

Keywords: fractional Kolmogorov-Petrovsky-Piskunov equation (FKPP); reaction-diffusion equation; chebyshev wavelet (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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