Revisited Fisher's equation in a new outlook: A fractional derivative approach

Marwan Alquran, Kamel Al-Khaled, Tridip Sardar, Joydev Chattopadhyay

Research output: Contribution to journalArticle

31 Citations (Scopus)

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 languageEnglish
Pages (from-to)81-93
Number of pages13
JournalPhysica A: Statistical Mechanics and its Applications
Volume438
DOIs
Publication statusPublished - Jul 17 2015

Fingerprint

Fisher Equation
Fractional Derivative
Survivability
birds
collocation
test stands
power series
Collocation
Power series
Testbed
genes
Difference Method
Numerical Study
Finite Difference
Approximate Solution
Fractional
Model
Gene
intervals
Interval

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 journalArticle

Alquran, Marwan ; Al-Khaled, Kamel ; Sardar, Tridip ; Chattopadhyay, Joydev. / Revisited Fisher's equation in a new outlook : A fractional derivative approach. In: Physica A: Statistical Mechanics and its Applications. 2015 ; Vol. 438. pp. 81-93.
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