### 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 |
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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 |

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

Prozorov, A. A., Trifonov, A. Y., & Shapovalov, A. V. (2015). Elementary particle physics and field theory: Asymptotic behavior of the one-dimensional fisher–kolmogorov–petrovskii–piskunov equation with anomalouos diffusion.

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