Planar System-Masses in an Equilateral Triangle: Numerical Study within
Fractional Calculus

Băleanu, Dumitru; Ghanbari, Behzad; Asad, Jihad; Jajarmi, Amin; Pirouz, Hassan Mohammadi

doi:10.32604/cmes.2020.010236

Cited by 62 publications

(59 citation statements)

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“…However, for highly oscillatory problems, the splitting error is too large and Magnus-type integrators are again to be preferred. Our findings may also have an impact on the study of time-dependent differential equations of other classes such as differential-algebraic equations [ 15 ], functional and stochastic differential equations [ 34 ], or fractional differential equations [ 29 , 38 ], see also [ 13 , 14 ].…”

Section: Discussionmentioning

confidence: 95%

Adaptive Time Propagation for Time-dependent Schrödinger equations

Auzinger

Hofstätter

Koch

et al. 2020

Int. J. Appl. Comput. Math

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We compare adaptive time integrators for the numerical solution of linear Schrödinger equations where the Hamiltonian explicitly depends on time. The approximation methods considered are splitting methods, where the time variable is split off and advanced separately, and commutator-free Magnus-type methods. The time-steps are chosen adaptively based on asymptotically correct estimators of the local error in both cases. It is found that splitting methods are more efficient when the Hamiltonian naturally suggests a separation into kinetic and potential part, whereas Magnus-type integrators excel when the structure of the problem only allows to advance the time variable separately.

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Section: Discussionmentioning

confidence: 95%

Adaptive Time Propagation for Time-dependent Schrödinger equations

Auzinger

Hofstätter

Koch

et al. 2020

Int. J. Appl. Comput. Math

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“…Individuals may transmit the infection at any stage with the transmission rates

and

respectively [7] , [8] , [13] , [19] . The formulation of model is considered as a system of differential equations and the outcome therefore indicates the prospective values of every portion [9] , [10] , [47] , [57] , [59] . It does not take into account stochastic events, and so the epidemic cannot go extinct even when it gets to very low values (except when an intervention is stopped, at which case the number of individuals in each state is rounded to the nearest integer).…”

Section: Introductionmentioning

confidence: 99%

COVID-19: Perturbation dynamics resulting chaos to stable with seasonality transmission

Batabyal

2021

Chaos, Solitons & Fractals

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The outbreak of coronavirus is spreading at an unprecedented rate to the human populations and taking several thousands of life all over the globe. In this paper, an extension of the well-known susceptible-exposed-infected-recovered (SEIR) family of compartmental model has been introduced with seasonality transmission of SARS-CoV-2. The stability analysis of the coronavirus depends on changing of its basic reproductive ratio. The progress rate of the virus in critical infected cases and the recovery rate have major roles to control this epidemic. Selecting the appropriate critical parameter from the Turing domain, the stability properties of existing patterns is obtained. The outcomes of theoretical studies, which are illustrated via Hopf bifurcation and Turing instabilities, yield the result of numerical simulations around the critical parameter to forecast on controlling this fatal disease. Globally existing solutions of the model has been studied by introducing Tikhonov regularization. The impact of social distancing, lockdown of the country, self-isolation, home quarantine and the wariness of global public health system have significant influence on the parameters of the model system that can alter the effect of recovery rates, mortality rates and active contaminated cases with the progression of time in the real world.

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“…To the authors' knowledge, due to the complexity of VFO systems, the results are rare on this topic. In addition, many studies have been devoted to the simulation of the fraction order system in recent years, and a large number of methods have emerged and the theories have gradually improved [45][46][47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

Finite time stability and sliding mode control for uncertain variable fractional order nonlinear systems

Jiang

Zhao

et al. 2021

Adv Differ Equ

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This paper deals with the finite time stability and control for a class of uncertain variable fractional order nonlinear systems. The variable fractional Lyapunov direct method is developed to provide the basis for the stability proof of the system considered. The sliding mode control method is applied for robust control of uncertain variable fractional order systems; furthermore, the chattering phenomenon is avoided. And the finite time stability of the systems under control law is proved based on the proposed stability criterion. Finally, numerical simulations are proposed and the efficiency of the controller is verified.

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Planar System-Masses in an Equilateral Triangle: Numerical Study within Fractional Calculus

Cited by 62 publications

References 0 publications

Adaptive Time Propagation for Time-dependent Schrödinger equations

Adaptive Time Propagation for Time-dependent Schrödinger equations

COVID-19: Perturbation dynamics resulting chaos to stable with seasonality transmission

Finite time stability and sliding mode control for uncertain variable fractional order nonlinear systems

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