### Abstract

The well-known Fisher equation with fractional derivative is considered to provide some characteristics of memory embedded into the system. The modified model is analyzed both analytically and numerically. A comparatively new technique residual power series method is used for finding approximate solutions of the modified Fisher model. A new technique combining Sinc-collocation and finite difference method is used for numerical study. The abundance of the bird species Phalacrocorax carbois considered as a test bed to validate the model outcome using estimated parameters. We conjecture non-diffusive and diffusive fractional Fisher equation represents the same dynamics in the interval (memory index, α∈(0.8384,0.9986)). We also observe that when the value of memory index is close to zero, the solutions bifurcate and produce a wave-like pattern. We conclude that the survivability of the species increases for long range memory index. These findings are similar to Fisher observation and act in a similar fashion that advantageous genes do.

Original language | English |
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Pages (from-to) | 81-93 |

Number of pages | 13 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 438 |

DOIs | |

Publication status | Published - Jul 17 2015 |

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### Keywords

- Approximate solutions
- Fisher's equation
- Fractional differential equation
- Generalized Taylor series
- Residual power series
- Sinc method

### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistics and Probability

### Cite this

*Physica A: Statistical Mechanics and its Applications*,

*438*, 81-93. https://doi.org/10.1016/j.physa.2015.06.036