Browsing by Author "Karaagac, Berat"

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Citation - WoS: 19
Citation - Scopus: 21
Dynamics of Pattern Formation Process in Fractional-Order Super-Diffusive Processes: a Computational Approach
(Springer, 2021) Karaagac, Berat; Baleanu, Dumitru; Owolabi, Kolade M.; 56389
This paper explores the suitability of space fractional-order reaction-diffusion scenarios to model some emergent pattern formation in predator-prey models. Such fractional reaction-diffusion equations are obtained on the basis of a continuous-time random walk approach with spatial memory and local kinetic reaction. The classical space second-order derivative is changed by the fractional Laplacian case. We employ the Fourier spectral method to numerically approximate the fractional Laplacian and advance in time with the novel ETDRK4 method. In other to obtain guidelines on the correct choice of parameters when numerically simulating the full reaction-diffusion models, the local dynamics of the systems are considered. The biological wave scenarios of solutions are verified by presenting some numerical results in two dimensions to mimic some spatiotemporal dynamics such as spots, stripes and spiral patterns which has a lot of ecological implications.
Citation - WoS: 30
Citation - Scopus: 30
Pattern Formation in Superdiffusion Predator-Prey Problems With Integer- and Noninteger-Order Derivatives
(Wiley, 2021) Karaagac, Berat; Baleanu, Dumitru; Owolabi, Kolade M.; 56389
This paper focuses on the modeling and application of fractional derivative to model the interactions between two different species in which the one named predator depends on the other called prey solely for survival. The interaction between predator and prey has been one of the most intriguing and interesting subjects in applied mathematical biology and ecology. In the models, the classical reaction-diffusion equations subject to the Neumann boundary conditions are formulated on a finite but large domain x is an element of [0, L] by replacing the second-order spatial derivatives with the fractional Laplacian operator of order 1 < alpha <= 2, which is classified as superdiffusion process. We examine the resulting coupled reaction-diffusion models for linear stability analysis and derive conditions under which the spatial patterns is evolved. In a view to understand our theoretical findings, the species spatial interactions is described in one and two dimensions. Through numerical experiments, we observe that a number of patterns can arise, including Turing spots, spiral-like structures, and seemingly complex spatiotemporal distributions.