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
N1 - Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.
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
AN - SCOPUS:84937060549
SN - 0378-4371
VL - 438
SP - 81
EP - 93
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
ER -