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

Akinyemi, Lanre

doi:10.1007/s40314-020-01212-9

Cited by 56 publications

(22 citation statements)

References 47 publications

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“…Nevertheless, solving FPDEs is generally more complex than the clas-sical type since their operators are defined through integrals. There are many techniques proposed by many researchers to handle analytical and approximate solutions of nonlinear FPDEs such as the residual power series method [25][26][27][28], iterative Shehu transform method [29], Laplace decomposition method [30], q-homotopy analysis method [31][32][33][34], Adomian decomposition method [35], fractional reduced differential transform method [36,37], variational iteration method [38,39], homotopy analysis method [40], and other methods [41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Modified homotopy methods for generalized fractional perturbed Zakharov–Kuznetsov equation in dusty plasma

2021

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We propose a new modification of homotopy perturbation method (HPM) called the δ-homotopy perturbation transform method (δ-HPTM). This modification consists of the Laplace transform method, HPM, and a control parameter δ. This control convergence parameter δ in this new modification helps in adjusting and controlling the convergence region of the series solution and overcome some limitations of HPM and HPTM. The δ-HPTM and q-homotopy analysis transform method (q-HATM) are considered to study the generalized time-fractional perturbed $(3+1)$ ( 3 + 1 ) -dimensional Zakharov–Kuznetsov equation with Caputo fractional time derivative. This equation describes nonlinear dust-ion-acoustic waves in the magnetized two-ion-temperature dusty plasmas. The selection of an appropriate value of δ in δ-HPTM and the auxiliary parameters n and ħ in q-HATM gives a guaranteed convergence of series solution, but the difference between the two techniques is that the embedding parameter p in δ-HPTM varies from zero to nonzero δ, whereas the embedding parameter q in q-HATM varies from zero to $\frac{1}{n}, n\geq{1}$ 1 n , n ≥ 1 . We examine the effect of fractional order on the considered problem and present the error estimate when compared with exact solution. The outcomes reveal complete reliability and efficiency of the proposed algorithm for solving various types of physical models arising in sciences and engineering. Furthermore, we present the convergence and error analysis of the two methods.

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Section: Introductionmentioning

confidence: 99%

Modified homotopy methods for generalized fractional perturbed Zakharov–Kuznetsov equation in dusty plasma

2021

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“…Besides, it's one of the trending topics for scientists and engineers to obtain solutions for nonlinear PDE. For solving them, there are many analytical and numerical methods developed, such as the differential transform method [1], the unified method [2], the generalized exponential rational function method [3], the variational iteration method [4,5], the first integral method [6,7], the q-homotopy analysis method [8,9], the Riccati equation method [10], the Bernoulli collocation method [11], the residual power series method [12,13], the Euler matrix method [14], the iterative shehu transform method [15], the Decomposition Method [16,17], the sub-equation method [18], the (G ′ /G)-expansion method [19,20], the modified simple equation method [21,22], the tanh-function method [23,24], the solitary wave Ansatz Method [25,26], and so on.…”

Section: Introductionmentioning

confidence: 99%

Optical singular and dark solitons to the nonlinear Schrodinger equation in magneto-optic waveguides with anti-cubic nonlinearity.

Mathanaranjan

Rezazadeh

Şenol

et al. 2021

Preprint

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The present paper aims to investigate the coupled nonlinear Schrodinger equation (NLSE) in magneto-optic waveguides having anti-cubic (AC) law nonlinearity. The solitons secured to magneto-optic waveguides with AC law nonlinearity are extremely useful to fiber-optic transmission technology. Three constructive techniques, namely, the (G'/G)-expansion method, the modified simple equation method (MSEM), and the extended tanh-function method are utilized to find the exact soliton solutions of this model. Consequently, dark, singular and combined dark-singular soliton solutions are obtained. The behaviours of soliton solutions are presented by 3D and 2D plots.

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“…Fractional calculus, which is a generalization of differentiation and integration of integer order, has been proposed to overcome many of the restrictions associated with integer order derivatives. Beyond biological systems, noninteger order derivatives have been successfully used to model physical phenomena in medicine, physics, image processing, optimization, electrodynamics, nanotechnology, biotechnology, engineering in general, and many more, see [10][11][12][13][14][15][16][17][18][19] [20][21][22], Laplace analysis method [23], homotopy analysis method [24][25][26][27][28], Adomian decomposition method [29], differential transformation method [30], perturbation-iteration algorithm [31], iterative Shehu transform method [32], residual power series method [33][34][35][36][37][38][39][40][41], and q-homotopy analysis transform method in [42][43][44][45].…”

Section: Introductionmentioning

confidence: 99%

“…Though every model should seek to use fractional calculus when introducing a new model, solving such a model is known to be very difficult and requires strong numerical or analytical techniques. Some of the methods used in the literature are homotopy perturbation method [ 20 – 22 ], Laplace analysis method [ 23 ], homotopy analysis method [ 24 – 28 ], Adomian decomposition method [ 29 ], differential transformation method [ 30 ], perturbation-iteration algorithm [ 31 ], iterative Shehu transform method [ 32 ], residual power series method [ 33 – 41 ], and q-homotopy analysis transform method in [ 42 – 45 ].…”

Section: Introductionmentioning

confidence: 99%

A fractional order approach to modeling and simulations of the novel COVID-19

et al. 2020

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The novel coronavirus (SARS-CoV-2), or COVID-19, has emerged and spread at fast speed globally; the disease has become an unprecedented threat to public health worldwide. It is one of the greatest public health challenges in modern times, with no proven cure or vaccine. In this paper, our focus is on a fractional order approach to modeling and simulations of the novel COVID-19. We introduce a fractional type susceptible–exposed–infected–recovered (SEIR) model to gain insight into the ongoing pandemic. Our proposed model incorporates transmission rate, testing rates, and transition rate (from asymptomatic to symptomatic population groups) for a holistic study of the coronavirus disease. The impacts of these parameters on the dynamics of the solution profiles for the disease are simulated and discussed in detail. Furthermore, across all the different parameters, the effects of the fractional order derivative are also simulated and discussed in detail. Various simulations carried out enable us gain deep insights into the dynamics of the spread of COVID-19. The simulation results confirm that fractional calculus is an appropriate tool in modeling the spread of a complex infectious disease such as the novel COVID-19. In the absence of vaccine and treatment, our analysis strongly supports the significance reduction in the transmission rate as a valuable strategy to curb the spread of the virus. Our results suggest that tracing and moving testing up has an important benefit. It reduces the number of infected individuals in the general public and thereby reduces the spread of the pandemic. Once the infected individuals are identified and isolated, the interaction between susceptible and infected individuals diminishes and transmission reduces. Furthermore, aggressive testing is also highly recommended.

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

Cited by 56 publications

References 47 publications

Modified homotopy methods for generalized fractional perturbed Zakharov–Kuznetsov equation in dusty plasma

Modified homotopy methods for generalized fractional perturbed Zakharov–Kuznetsov equation in dusty plasma

Optical singular and dark solitons to the nonlinear Schrodinger equation in magneto-optic waveguides with anti-cubic nonlinearity.

A fractional order approach to modeling and simulations of the novel COVID-19

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