THERMAL SCIENCE

International Scientific Journal

Bo Xu

,

Yufeng Zhang

,

Sheng Zhang

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
fractional derivative, fractional KPP equation, analytical method, exact solution, operator solution, kink-soliton solution
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 No. 3, PAGES [2161 - 2168]
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Analytical methods for non-linear fractional Kolmogorov-Petrovskii-Piskunov equation: Soliton solution and operator solution

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence