Numerical investigations for time-fractional nonlinear model arise in physics

Jaradat, Ali; Noorani, Mohd Salmi Md; Alquran, Marwan; Jaradat, H. M.

doi:10.1016/j.rinp.2018.01.049

Cited by 4 publications

(1 citation statement)

References 11 publications

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“…• The first case is when γ = β = 0. This case has also been considered by Jaradat et al (2018a) by means of generalized Taylor power series method with different initial conditions. • The second case when γ = λ and β = 1 is study for the first time.…”

Section: Introductionmentioning

confidence: 99%

A fractional analysis of Noyes–Field model for the nonlinear Belousov–Zhabotinsky reaction

Akinyemi

2020

Comp. Appl. Math.

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Nonlinear phenomena play an essential role in various field of natural sciences and engineering. In particular, the nonlinear chemical reactions are observed in various domains, as, for instance, in biological and chemical physics. For this reason, it is important to investigate the solution to this nonlinear phenomenon. This article investigates numerical solutions to a nonlinear oscillatory system called the Belousov-Zhabotinsky with Caputo fractional-time derivative. The simplified Noyes-Field fractional model reads D μ t p = ξ 1 p x x + βδw + p − p 2 − δ pw, 0 < μ ≤ 1, D μ t w = ξ 2 w x x + γ w − λ pw, where ξ 1 and ξ 2 are the diffusing constants for the concentration p and w respectively, γ and β are given constants, λ = 1 and δ are positive parameters. The two iterative techniques used in this work are the fractional reduced differential transform method and q-homotopy analysis transform method. The outcomes using these two methods reveal an efficient numerical solution with high accuracy and minimal computations. Furthermore, to better understand the effect of the fractional order, we present the solution profiles which demonstrate the behavior of the obtained results.

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Section: Introductionmentioning

confidence: 99%