### 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 |
---|---|

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

**Revisited Fisher's equation in a new outlook : A fractional derivative approach.** / Alquran, Marwan; Al-Khaled, Kamel; Sardar, Tridip; Chattopadhyay, Joydev.

Research output: Contribution to journal › Article

*Physica A: Statistical Mechanics and its Applications*, vol. 438, pp. 81-93. https://doi.org/10.1016/j.physa.2015.06.036

}

TY - JOUR

T1 - Revisited Fisher's equation in a new outlook

T2 - A fractional derivative approach

AU - Alquran, Marwan

AU - Al-Khaled, Kamel

AU - Sardar, Tridip

AU - Chattopadhyay, Joydev

PY - 2015/7/17

Y1 - 2015/7/17

N2 - 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.

AB - 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.

KW - Approximate solutions

KW - Fisher's equation

KW - Fractional differential equation

KW - Generalized Taylor series

KW - Residual power series

KW - Sinc method

UR - http://www.scopus.com/inward/record.url?scp=84937060549&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937060549&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2015.06.036

DO - 10.1016/j.physa.2015.06.036

M3 - Article

AN - SCOPUS:84937060549

VL - 438

SP - 81

EP - 93

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

ER -