Dynamics of multi-pulse splitting process in one-dimensional Gray-Scott system with fractional order operator

Kolade M. Owolabi and Berat Karaagac

Chaos, Solitons & Fractals, 2020, vol. 136, issue C

Abstract: In this paper, the dynamic process of pulse-splitting patterns is reported in fractional medium. In the classical Gray-Scott system, the integer-order derivative is replaced with the known Atangana-Baleanu fractional order derivative in the sense of Caputo. mathematical analysis such as the existence of stationary solutions for pulse-splitting process, existence and uniqueness of solutions for the fractional system are presented. The beauty of the work is further demonstrated by presenting numerical results for different values of γ in one dimensional space. We deduced from the numerical experiments that pulse-splitting patterns in both integer and noninteger order scenarios are almost the same.

Keywords: ABC operator; Fractional derivative; Reaction-diffusion system; Numerical simulation; Pulse formation (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:136:y:2020:i:c:s0960077920302356

DOI: 10.1016/j.chaos.2020.109835

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