### Abstract

Asymptotic solutions of the nonlocal, one-dimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation with fractional derivatives in the diffusion operator are constructed. The fractional derivative is defined in accordance with the approaches of Weyl, Grünwald–Letnilkov, and Liouville. Asymptotic solutions are constructed in a class of functions that are a perturbation of the found exact quasistationary solution and tend at large times to this quasistationary solution. It is shown that the presence of fractional derivatives leads to drift of the center of mass of the initial distribution and breaks its symmetry.

Original language | English |
---|---|

Article number | A019 |

Pages (from-to) | 399-409 |

Number of pages | 11 |

Journal | Russian Physics Journal |

Volume | 58 |

Issue number | 3 |

DOIs | |

Publication status | Published - 17 Jul 2015 |

### Fingerprint

### Keywords

- Anomalous diffusion
- Asymmetric solutions
- Nonlocal Fisher–KPP equation

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Russian Physics Journal*,

*58*(3), 399-409. [A019]. https://doi.org/10.1007/s11182-015-0514-9

**Elementary particle physics and field theory : Asymptotic behavior of the one-dimensional fisher–kolmogorov–petrovskii–piskunov equation with anomalouos diffusion.** / Prozorov, Alexander Andreevich; Trifonov, A. Yu; Shapovalov, Aleksandr Vasilievich.

Research output: Contribution to journal › Article

*Russian Physics Journal*, vol. 58, no. 3, A019, pp. 399-409. https://doi.org/10.1007/s11182-015-0514-9

}

TY - JOUR

T1 - Elementary particle physics and field theory

T2 - Asymptotic behavior of the one-dimensional fisher–kolmogorov–petrovskii–piskunov equation with anomalouos diffusion

AU - Prozorov, Alexander Andreevich

AU - Trifonov, A. Yu

AU - Shapovalov, Aleksandr Vasilievich

PY - 2015/7/17

Y1 - 2015/7/17

N2 - Asymptotic solutions of the nonlocal, one-dimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation with fractional derivatives in the diffusion operator are constructed. The fractional derivative is defined in accordance with the approaches of Weyl, Grünwald–Letnilkov, and Liouville. Asymptotic solutions are constructed in a class of functions that are a perturbation of the found exact quasistationary solution and tend at large times to this quasistationary solution. It is shown that the presence of fractional derivatives leads to drift of the center of mass of the initial distribution and breaks its symmetry.

AB - Asymptotic solutions of the nonlocal, one-dimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation with fractional derivatives in the diffusion operator are constructed. The fractional derivative is defined in accordance with the approaches of Weyl, Grünwald–Letnilkov, and Liouville. Asymptotic solutions are constructed in a class of functions that are a perturbation of the found exact quasistationary solution and tend at large times to this quasistationary solution. It is shown that the presence of fractional derivatives leads to drift of the center of mass of the initial distribution and breaks its symmetry.

KW - Anomalous diffusion

KW - Asymmetric solutions

KW - Nonlocal Fisher–KPP equation

UR - http://www.scopus.com/inward/record.url?scp=84937046732&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937046732&partnerID=8YFLogxK

U2 - 10.1007/s11182-015-0514-9

DO - 10.1007/s11182-015-0514-9

M3 - Article

VL - 58

SP - 399

EP - 409

JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

IS - 3

M1 - A019

ER -