EXACT TRAVELLING WAVE SOLUTIONS OF REACTION-DIFFUSION MODELS OF FRACTIONAL ORDER

Jin Hyuk Choi; Hyunsoo Kim; Rathinasamy Sakthivel

doi:10.11948/2017016

2017 Volume 7 Issue 1

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Jin Hyuk Choi, Hyunsoo Kim, Rathinasamy Sakthivel. EXACT TRAVELLING WAVE SOLUTIONS OF REACTION-DIFFUSION MODELS OF FRACTIONAL ORDER[J]. Journal of Applied Analysis & Computation, 2017, 7(1): 236-248. doi: 10.11948/2017016

Citation:

Jin Hyuk Choi, Hyunsoo Kim, Rathinasamy Sakthivel. EXACT TRAVELLING WAVE SOLUTIONS OF REACTION-DIFFUSION MODELS OF FRACTIONAL ORDER[J]. Journal of Applied Analysis & Computation, 2017, 7(1): 236-248. doi: 10.11948/2017016

EXACT TRAVELLING WAVE SOLUTIONS OF REACTION-DIFFUSION MODELS OF FRACTIONAL ORDER

1 Humanitas College, Kyung Hee University, Yongin 446-701, Republic of Korea;
2 Department of Mathematics, Sungkyunkwan University, Suwon-440-746, Republic of Korea

Abstract

Abstract

Reaction-diffusion models are used in different areas of chemistry problems. Also, coupled reaction-diffusion systems describing the spatio-temporal 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.
- Reaction-diffusion models /
- fractional calculus /
- exact solution /
- Q-function method
MSC: 35Q51;35Q53

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References

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