Resonance and bifurcation of fractional quintic Mathieu–Duffing system

Zhang, Jiale; Xie, Jiaquan; Shi, Wei; Huo, Yiting; Ren, Zhongkai; He, Dongping

doi:10.1063/5.0138864

Cited by 38 publications

(17 citation statements)

References 47 publications

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“…Because of this, FPDEs are being used more often in scientific research. This has made it easier to create new theoretical frameworks and experimental plans that can better capture the complex behaviors of natural systems [5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Investigating Families of Soliton Solutions for the Complex Structured Coupled Fractional Biswas–Arshed Model in Birefringent Fibers Using a Novel Analytical Technique

et al. 2023

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This research uses a novel analytical method known as the modified Extended Direct Algebraic Method (mEDAM) to explore families of soliton solutions for the complex structured Coupled Fractional Biswas–Arshed Model (CFBAM) in Birefringent Fibers. The Direct Algebraic Method (DAM) is extended by the mEDAM’s methodology to compute more analytical solutions that would otherwise be difficult to acquire. We use this method to derive several families of soliton solutions and examine their characteristics. We also look at how different model parameters, such as amplitude, width, and propagation speed, affect the dynamics of soliton. Our use of 2D and 3D graphics to illustrate the soliton solutions also makes it possible to see the soliton dynamics more clearly. The outcomes also demonstrate that the method suggested has proven successful in producing soliton solutions for intricate structures such as the CFBAM.

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Section: Introductionmentioning

confidence: 99%

Investigating Families of Soliton Solutions for the Complex Structured Coupled Fractional Biswas–Arshed Model in Birefringent Fibers Using a Novel Analytical Technique

et al. 2023

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“…These equations have drawn a lot of attention due to their outstanding simulation over traditional integer-order differential equations for a variety of physical and biological phenomena. They are often used to explain the viscous materials, system of control, and signal analysis in a variety of fields, including physics, engineering, biology, economics, and much more [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of Time-Fractional Porous Media and Heat Transfer Equations Using a Semi-Analytical Approach

et al. 2023

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In nature, symmetry is all around us. The symmetry framework represents integer partial differential equations and their fractional order in the sense of Caputo derivatives. This article suggests a semi-analytical approach based on Aboodh transform (AT) and the homotopy perturbation scheme (HPS) for achieving the approximate solution of time-fractional porous media and heat transfer equations. The AT converts the fractional problems into simple ones and obtains the recurrence relation without any discretization or assumption. This nonlinear recurrence relation can be decomposed via the use of the HPS to obtain the iterations in terms of series solutions. The initial conditions play an important role in determining the successive iterations and yields towards the exact solution. We provide some numerical applications to analyze the accuracy of this proposed scheme and show that the performance of our scheme has strong agreement with the exact results.

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“…Tey studied the local and global dynamics of their proposed model and provided the most sensitive parameters that can increase or decrease the threshold quantity. Te anxiety causes during the COVID-19 outbreak to people has been studied in [32], the bifurcation analysis involved in the fractional system in [33], and medical imaging in [34]. Some more applications can be seen in [35,36].…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling and Analysis of COVID-19 Infection: Application to the Kingdom of Saudi Arabia Data

Alzahrani,

Khan

2023

Journal of Mathematics

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To evaluate the probable effects of the COVID-19 outbreak on Saudi Arabia, a novel dynamical model is developed. Using the most recent instances of COVID-19 infection that have been reported in Saudi Arabia, we examine the roles of quarantine and hospitalization. The model’s mathematical outcomes are displayed. The model’s infection-free equilibrium is displayed, and asymptotically, it is determined to be both locally and globally stable. We demonstrate that the model is locally asymptotically stable (LAS) for the basic reproduction R 0 < 1 . The model is globally asymptotically stable (GAS) when R 0 ≤ 1 . To estimate the model parameters, recent COVID-19 instances in KSA that began between May 1, 2022, and August 4, 2022, are taken into account. We achieve the needed data fitting considering the approach of nonlinear least square, and we demonstrate that the predicted basic reproduction number is R 0 ≈ 1.2988 . Graphical representations of the calculated parameters and their effects on disease eradication are provided. The findings show that the most effective way to reduce the number of new instances of infection is to limit the contact of exposed, asymptomatic, symptomatic, and hospitalized people with vulnerable. The percentage of exposed people who are quarantined also plays a big part in lowering the number of infected cases.

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Resonance and bifurcation of fractional quintic Mathieu–Duffing system

Cited by 38 publications

References 47 publications

Investigating Families of Soliton Solutions for the Complex Structured Coupled Fractional Biswas–Arshed Model in Birefringent Fibers Using a Novel Analytical Technique

Investigating Families of Soliton Solutions for the Complex Structured Coupled Fractional Biswas–Arshed Model in Birefringent Fibers Using a Novel Analytical Technique

Numerical Analysis of Time-Fractional Porous Media and Heat Transfer Equations Using a Semi-Analytical Approach

Mathematical Modeling and Analysis of COVID-19 Infection: Application to the Kingdom of Saudi Arabia Data

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