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ANALYTICAL METHODS FOR NON-LINEAR FRACTIONAL KOLMOGOROV-PETROVSKII-PISKUNOV EQUATION Soliton Solution and Operator Solution.
- Source :
- Thermal Science; 2021, Vol. 25 Issue 3B, p2161-2168, 8p
- Publication Year :
- 2021
-
Abstract
- Kolmogorov-Petrovskii-Piskunov equation can be regarded as a generalized form of the Fitzhugh-Nagumo, Fisher and Huxley equations which have many applications in physics, chemistry and biology. In this paper, two fractional extended versions of the non-linear Kolmogorov-Petrovskii-Piskunov equation are solved by analytical methods. Firstly, a new and more general fractional derivative is defined and some properties of it are given. Secondly, a solution in the form of operator representation of the non-linear Kolmogorov-Petrovskii- Piskunov equation with the defined fractional derivative is obtained. Finally, some exact solutions including kink-soliton solution and other solutions of the non-linear Kolmogorov-Petrovskii-Piskunov equation with Khalil et al.'s fractional derivative and variable coefficients are obtained. It is shown that the fractional- order affects the propagation velocity of the obtained kink-soliton solution. [ABSTRACT FROM AUTHOR]
- Subjects :
- NONLINEAR equations
NONLINEAR operators
EQUATIONS
Subjects
Details
- Language :
- English
- ISSN :
- 03549836
- Volume :
- 25
- Issue :
- 3B
- Database :
- Complementary Index
- Journal :
- Thermal Science
- Publication Type :
- Academic Journal
- Accession number :
- 150627658
- Full Text :
- https://doi.org/10.2298/TSCI191123102X