Iterative methods for solving fourth‐ and sixth‐order time‐fractional Cahn‐Hillard equation

Akinyemi, Lanre; Iyiola, Olaniyi S.; Akpan, Udoh

doi:10.1002/mma.6173

Cited by 38 publications

(39 citation statements)

References 52 publications

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“…In [12] , [13] , [14] , [15] , discussed the exact and approximate solutions by using different numerical methods for various types of fractional differential equations (FDEs). They also described the error and convergence analysis.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a novel coronavirus (2019-nCOV) system with variable Caputo-Fabrizio fractional order

Verma

Kumar

2021

Chaos, Solitons & Fractals

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Highlights New variable fractional-order derivatives a novel coronavirus (2019-nCOV) system, namely, the variable Caputo-Fabrizio in Caputo sense for 2019-nCOV system. New existence and uniqueness results of the solution for the proposed 2019-nCOV system. Generalized Hyers-Ulam stability as well as the generalized Hyers-Ulam-Rassias stability.

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Section: Introductionmentioning

confidence: 99%

Analysis of a novel coronavirus (2019-nCOV) system with variable Caputo-Fabrizio fractional order

Verma

Kumar

2021

Chaos, Solitons & Fractals

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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%

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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“…The search for a better way to expand the convergence region led to the modification of HAM, called q-HAM, more of a general method than HAM [48]. Many authors have taken advantage of q-HAM and used it to solve nonlinear fractional partial differential equations [49][50][51][52][53][54][55]. The q-HATM was proposed by Singh et al [56] and did not require any form of discretization, linearization, or perturbation as compared to other methods.…”

Section: Introductionmentioning

confidence: 99%

A reliable technique to study nonlinear time-fractional coupled Korteweg–de Vries equations

Akinyemi

Iyiola

2020

Adv Differ Equ

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This paper employs an efficient technique, namely q-homotopy analysis transform method, to study a nonlinear coupled system of equations with Caputo fractional-time derivative. The nonlinear fractional coupled systems studied in this present investigation are the generalized Hirota-Satsuma coupled with KdV, the coupled KdV, and the modified coupled KdV equations which are used as a model in nonlinear physical phenomena arising in biology, chemistry, physics, and engineering. The series solution obtained using this method is proved to be reliable and accurate with minimal computations. Several numerical comparisons are made with well-known analytical methods and the exact solutions when α = 1. It is evident from the results obtained that the proposed method outperformed other methods in handling the coupled systems considered in this paper. The effect of the fractional order on the problem considered is investigated, and the error estimate when compared with exact solution is presented.Here, we present some useful definitions, properties, and notations that will be used in this work. Definition 2.1 The Riemann-Liouville (R-L) fractional integral of order α (α ≥ 0) of a function Q(x, t) ∈ C m , m ≥ -1, is given as [29, 63-65] J α Q(x, t) = 1 Γ (α) t 0

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Iterative methods for solving fourth‐ and sixth‐order time‐fractional Cahn‐Hillard equation

Cited by 38 publications

References 52 publications

Analysis of a novel coronavirus (2019-nCOV) system with variable Caputo-Fabrizio fractional order

Analysis of a novel coronavirus (2019-nCOV) system with variable Caputo-Fabrizio fractional order

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

A reliable technique to study nonlinear time-fractional coupled Korteweg–de Vries equations

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