Numerical Investigation of Fractional‐Order Kawahara and Modified Kawahara Equations by a Semianalytical Method

Alhejaili, Weaam; Alhazmi, Sharifah E.; Nawaz, Rashid; Ali, Aatif; Asamoah, Joshua Kiddy K.; Zada, Laiq

doi:10.1155/2022/1985572

Cited by 8 publications

(2 citation statements)

References 30 publications

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“…In addition, mathematical representations that include fractional-order derivatives capture a broader spectrum of natural phenomena with increased validity and efficiency. Other fractional derivatives, such as the Riemann-Liouville, Caputo, Hilfer, Caputo Fabrizio, Atangana Baleanu, and Grünwald-Letnikov derivatives, have been proposed recently [4][5][6][7]. In the realm of fractional calculus, the Caputo fractional derivative stands as a foundational concept, facilitating the exploration of fractional differential equations (FDEs).…”

Section: Introductionmentioning

confidence: 99%

Solving the fractional Fornberg-Whitham equation within Caputo framework using the optimal auxiliary function method

Iqbal,

Hussain,

Nazim Tufail

et al. 2024

Phys. Scr.

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In this work, we solve the fractional-order Fornberg-Whitham (FW) problem in the context of the Caputo operator by using the Optimal Auxiliary Function Method. Tables and figures showing full numerical findings indicate the correctness and efficacy of this strategy. The results provide insights into the solution behavior of the FW equation and demonstrate the applicability of the Optimal Auxiliary Function Method. By giving insight on the behavior of the FW equation in a fractional context, this research advances the use of fractional calculus techniques in the solution of complicated differential equations.

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Section: Introductionmentioning

confidence: 99%

Solving the fractional Fornberg-Whitham equation within Caputo framework using the optimal auxiliary function method

Iqbal,

Hussain,

Nazim Tufail

et al. 2024

Phys. Scr.

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“…Further, recent papers have studied the nonlinear generalizations of Stokes-Darcy equations [32][33][34] by applying domain decomposition techniques, optimization methods, and mortar finite element methods. Other effective techniques should be noted, such as the optimal homotopy asymptotic method [35,36], which was successfully applied to studying nonlinear behaviors described by partial differential equations containing fractional-order time derivatives [37,38].…”

Section: Introductionmentioning

confidence: 99%

Numerical Method for Fractional-Order Generalization of the Stochastic Stokes–Darcy Model

Berdyshev,

Baigereyev,

Boranbek

2023

Mathematics

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This paper is aimed at efficient numerical implementation of the fractional-order generalization of the stochastic Stokes–Darcy model, which has important scientific, applied, and economic significance in hydrology, the oil industry, and biomedicine. The essence of this generalization of the stochastic model is the introduction of fractional time derivatives in the sense of Caputo’s definition to take into account long-term changes in the properties of media. An efficient numerical method for the implementation of the fractional-order Stokes–Darcy model is proposed, which is based on the use of a higher-order approximation formula for the fractional derivative, higher-order finite difference relations, and a finite element approximation of the problem in the spatial direction. In the paper, a rigorous theoretical analysis of the stability and convergence of the proposed numerical method is carried out, which is confirmed by numerous computational experiments. Further, the proposed method is applied to the implementation of the fractional-order stochastic Stokes–Darcy model using an ensemble technique, in which the approximation is carried out in such a way that the resulting systems of linear equations have the same coefficient matrix for all realizations. Furthermore, evaluation of the discrete fractional derivatives is carried out with the use of parallel threads. The efficiency of applying both approaches has been demonstrated in numerical tests.

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Spatiotemporal analysis of Zika virus transmission dynamics incorporating human mobility and seasonal variations using modified homotopy perturbation method

Alaje,

Olayiwola,

Odeleye

2024

J.Umm Al-Qura Univ. Appll. Sci.

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This study employed a mathematical model to evaluate how seasonal variations, vector dispersal, and mobility of people affect the spread of the Zika virus. The model's positive solutions, invariant zones, and solution existence and uniqueness were validated through proved theorems. The equilibria points were identified, and the basic reproduction number was calculated. The model was semi-analytically solved using a modified homotopy perturbation approach, and an applied convergence test proved that the solution converges. The simulation results indicated that under optimal breeding conditions, the density of healthy mosquitoes peaked in the fourth month. Two months later, increased mosquito dispersal and human carriers facilitated by favorable weather led to a rise in mosquito infectiousness, peaking between the fourth and eighth months due to significant seasonal effects, resulting in high Zika transmission. To effectively control mosquito populations and reduce Zika transmission, it is recommended that public health interventions focus on the critical periods spanning the third to eighth months.

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Numerical Investigation of Fractional‐Order Kawahara and Modified Kawahara Equations by a Semianalytical Method

Cited by 8 publications

References 30 publications

Solving the fractional Fornberg-Whitham equation within Caputo framework using the optimal auxiliary function method

Solving the fractional Fornberg-Whitham equation within Caputo framework using the optimal auxiliary function method

Numerical Method for Fractional-Order Generalization of the Stochastic Stokes–Darcy Model

Spatiotemporal analysis of Zika virus transmission dynamics incorporating human mobility and seasonal variations using modified homotopy perturbation method

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