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

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 de...

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Published in:Mathematics (Basel) 2019-09, Vol.7 (9), p.813
Main Authors: Korkiatsakul, Thanon, Koonprasert, Sanoe, Neamprem, Khomsan
Format: Article
Language:English
Subjects:
Boundary conditions
Calculus
Chebyshev approximation
chebyshev wavelet
Chemical reactions
Dirichlet problem
Exact solutions
Food science
fractional Kolmogorov-Petrovsky-Piskunov equation (FKPP)
Mathematical analysis
Polynomials
reaction-diffusion equation
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description 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.
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subjects Boundary conditions
Calculus
Chebyshev approximation
chebyshev wavelet
Chemical reactions
Dirichlet problem
Exact solutions
Food science
fractional Kolmogorov-Petrovsky-Piskunov equation (FKPP)
Mathematical analysis
Polynomials
reaction-diffusion equation
title New Analytical Solutions for Time-Fractional Kolmogorov-Petrovsky-Piskunov Equation with Variety of Initial Boundary Conditions
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