### Journals Information

Universal Journal of Computational Mathematics(CEASE PUBLICATION) Vol. 5(3), pp. 75 - 85
DOI: 10.13189/ujcmj.2017.050304
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## Fourier Spectral Method for Solving Fractional-order System

1 Department of Mathematical Sciences, Federal University of Technology, PMB 704, Akure, Ondo State, Nigeria
2 Department of Computer Engineering, Federal University of Technology, PMB 704, Akure, Ondo State, Nigeria

ABSTRACT

In this paper, we have studied a new fractional reaction-diffusion two-species system as an extension to the Rosenzweig-MacArthur reaction-diffusion di-trophic food chain system which models the spatial interactions between a prey and predator. To guarantee good working guidelines when numerically simulating the model, we first show that the system is locally asymptotically stable, as it provides good conditions and correct choice of ecological parameters to enhance a biologically meaningful result. We propose a fast and accurate method for numerical solutions of space fractional reaction-diffusion equations. The technique is based on Fourier spectral method in space and exponential integrator scheme in time. The complexity of fractional derivative index in fractional reaction diffusion model is numerically formulated and graphically displayed in one-, two- and three-dimensions.

KEYWORDS
Fourier Spectral Method, Exponential Integrator, Reaction-diffusion System, Oscillations, Rosenzweig-macarthur Model, Stability Analysis

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Kolade M. Owolabi , Ayodeji A. Adejola , "Fourier Spectral Method for Solving Fractional-order System," Universal Journal of Computational Mathematics(CEASE PUBLICATION), Vol. 5, No. 3, pp. 75 - 85, 2017. DOI: 10.13189/ujcmj.2017.050304.

(b). APA Format:
Kolade M. Owolabi , Ayodeji A. Adejola (2017). Fourier Spectral Method for Solving Fractional-order System. Universal Journal of Computational Mathematics(CEASE PUBLICATION), 5(3), 75 - 85. DOI: 10.13189/ujcmj.2017.050304.