Nonlinear non-Markovian model of subdiffusive transport with chemotaxis

Akram Al-Sabbagh (Collaborator)

Research output: Contribution to journalArticlepeer-review

Abstract

The purpose of this work is to propose a nonlinear non-Markovian model of subdiffusive transport that involves chemotactic substance affecting the cells at all time, not only during the jump. This leads the random waiting time to be dependent on the chemotactic gradient, making the escape rates also dependent on the gradient as well as the nonlinear density dependence. We systematically derive subdiffusive fractional master equation, then we consider the diffusive limit of the fractional master equation. We finally solve the resulting fractional subdiffusive master equation stationery and analyse the role of the chemotactic gradient in the resulting stationary density with a constant and a quadratic chemotactic gradient.
Original languageEnglish
Pages (from-to)181-197
Number of pages16
JournalInternational Journal of Enhanced Research in Science Technology & Engineering
Volume5
Issue number2
Publication statusPublished - Feb 2016

Keywords

  • Anomalous Subdiffusion, Chemotaxis

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