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

34 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

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

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