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ANALYTICAL METHODS FOR NON-LINEAR FRACTIONAL KOLMOGOROV-PETROVSKII-PISKUNOV EQUATION: SOLITON SOLUTION AND OPERATOR SOLUTION

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 ex-tended 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.
KEYWORDS
PAPER SUBMITTED: 2019-11-23
PAPER REVISED: 2020-07-10
PAPER ACCEPTED: 2020-07-10
PUBLISHED ONLINE: 2021-03-27
DOI REFERENCE: https://doi.org/10.2298/TSCI191123102X
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 3, PAGES [2161 - 2168]
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