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
Revisited Fisher's equation in a new outlook : A fractional derivative approach. / Alquran, Marwan; Al-Khaled, Kamel; Sardar, Tridip; Chattopadhyay, Joydev.
In: Physica A: Statistical Mechanics and its Applications, Vol. 438, 17.07.2015, p. 81-93.Research output: Contribution to journal › Article
}
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
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U2 - 10.1016/j.physa.2015.06.036
DO - 10.1016/j.physa.2015.06.036
M3 - Article
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 -