Fractal dynamics of solution moments for the KPP–Fisher equation

The paper focuses on the KPP–Fisher equation (named after Andrey Kolmogorov, Ivan Petrovskii, Nikolai Piskunov and Ronald Fisher) with non-local competitive losses and fractal time derivative which is considered in terms of F α -calculus on the Cantor set dimension 0 < α < 1. A dynamic system...

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Bibliographic Details
Published inRussian physics journal Vol. 67; no. 11; pp. 1827 - 1837
Main Authors Shapovalov, A. V., Siniukov, S. A.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.11.2024
Springer Nature B.V
Subjects
Condensed Matter Physics
Derivatives
Dynamical systems
Fractals
Hadrons
Heavy Ions
Lasers
Mathematical and Computational Physics
Nuclear Physics
Optical Devices
Optics
Parameters
Photonics
Physics
Physics and Astronomy
Theoretical
Semiclassical asymptotics
Fractal calculus
KPP–Fisher equation
Fractal time derivative
530.182
Dynamic system of moments
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Summary:The paper focuses on the KPP–Fisher equation (named after Andrey Kolmogorov, Ivan Petrovskii, Nikolai Piskunov and Ronald Fisher) with non-local competitive losses and fractal time derivative which is considered in terms of F α -calculus on the Cantor set dimension 0 < α < 1. A dynamic system with the fractal time derivative relating to the moments not higher than the second-order for the KPP–Fisher equation, is deduced in the semiclassical approximation with respect to the small diffusion parameter in the class of trajectory-concentrated functions. An example is given to the dynamic system of solution moments constructed and explored for various values of α parameter.
Bibliography:ObjectType-Article-1
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ISSN:1064-8887
1573-9228
DOI:10.1007/s11182-024-03319-6