Open AccessEXACT TRAVELLING WAVE SOLUTIONS OF REACTION-DIFFUSION MODELS OF FRACTIONAL ORDER
Author(s) -
Jin Hyuk Choi,
Hyunsoo Kim,
R. Sakthivel
Publication year - 2017
Publication title -
journal of applied analysis and computation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.55
H-Index - 21
eISSN - 2158-5644
pISSN - 2156-907X
DOI - 10.11948/2017016
Subject(s) - allee effect , traveling wave , reaction–diffusion system , competition model , competition (biology) , diffusion , order (exchange) , population , mathematics , statistical physics , exact solutions in general relativity , biological dispersal , population model , mathematical analysis , ecology , physics , thermodynamics , biology , economics , demography , profit (economics) , finance , sociology , microeconomics
Reaction-diffusion models are used in different areas of chemistry problems. Also, coupled reaction-diffusion systems describing the spatiotemporal dynamics of competition models have been widely applied in many real world problems. In this paper, we consider a coupled fractional system with diffusion and competition terms in ecology, and reaction-diffusion growth model of fractional order with Allee effect describing and analyzing the spread dynamic of a single population under different dispersal and growth rates. Finding the exact solutions of such models are very helpful in the theories and numerical studies. Exact traveling wave solutions of the above reaction-diffusion models are found by means of the Q-function method. Moreover, graphic illustrations in two and three dimensional plots of some of the obtained solutions are also given to predict their behaviours.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom