New features of the fractional Euler-Lagrange equations for a physical system within non-singular derivative operator

Băleanu, Dumitru; Sajjadi, Samaneh Sadat; Jajarmi, Amin; Asad, Jihad

doi:10.1140/epjp/i2019-12561-x

Cited by 91 publications

(55 citation statements)

References 34 publications

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“…Fractional calculus has memory function, which ensures revealing the influences of historical information on present and future, and hence is beneficial to improving the quality of control. Fractional calculus has been used to model the real world problems [1][2][3][4][5][6][7]. It is playing a very important role in the field of science, engineering, finance, communication, epidemic, etc.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of a fractional-order SIS model on complex networks with linear treatment function

et al. 2019

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In recent years, many research works have been focusing on the propagation dynamics of infectious diseases in complex networks, and some interesting results have been obtained. The main purpose of this paper is to investigate the stability of a fractional SIS model on complex networks with linear treatment function. Based on the basic reproduction number, the stability of the disease-free equilibrium point and the endemic equilibrium point is analyzed in detail. That is, when R 0 ≤ 1, the disease-free equilibrium point is globally asymptotically stable and the disease will die out ultimately; when R 0 > 1, there exists a unique endemic equilibrium point, and both the disease-free equilibrium point and the endemic equilibrium point are stable and the disease will not spread to all individuals. Finally, numerical simulations are presented to demonstrate the theoretical results. Moreover, the influence of the fractional-order parameter and the coefficient of the linear treatment function on the decay rate of the infectious is depicted separately.

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Section: Introductionmentioning

confidence: 99%

Stability analysis of a fractional-order SIS model on complex networks with linear treatment function

et al. 2019

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“…The biggest important advantage of using fractional partial differential equations in mathematical modeling is their non-local property in the sense that the next state of the system depends not only upon its current state but also upon all of its proceeding states. The fractional-order models are more adequate than the integralorder models to describe the memory and hereditary properties of different substances [11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Filter regularization method for a time-fractional inverse advection–dispersion problem

Liu

Feng

2019

Adv Differ Equ

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“…However, DPL constitutive relation can not describe abnormal diffusion or diffusion in biological tissues. On the other hand, fractional calculus has become a hot topic because of the global dependency and nonlocal property of the fractional derivatives . The new trends of nanotechnology and fractional calculus were discussed .…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, fractional calculus has become a hot topic because of the global dependency and nonlocal property of the fractional derivatives. [8][9][10][11] The new trends of nanotechnology and fractional calculus were discussed. 12 Fractional Hamiltonian analysis of irregular systems was discussed.…”

Section: Introductionmentioning

confidence: 99%

Efficient and accurate spectral method for the time‐fractional dual‐phase‐lag heat transfer model and its parameter estimation

Zheng

Jiang

Zhang

2019

Math Methods in App Sciences

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In the current paper, a heat transfer model is suggested based on a time‐fractional dual‐phase‐lag (DPL) model. We discuss the model in two parts, the direct problem and the inverse problem. Firstly, for solving it, the finite difference/Legendre spectral method is constructed. In the temporal direction, we employ the weighted and shifted Grünwald approximation, which can achieve second order convergence. In the spatial direction, the Legendre spectral method is used, it can obtain spectral accuracy. The stability and convergence are theoretically analyzed. For the inverse problem, the Bayesian method is used to construct an algorithm to estimate the four parameters for the model, namely, the time‐fractional order α, the time‐fractional order β, the delay time τT, and the relaxation time τq. Next, numerical experiments are provided to demonstrate the effectiveness of our scheme, with the values of τq and τT for processed meat employed. We also make a comparison with another method. The data obtained for the direct problem are used in the parameter estimation. The paper provides an accurate and efficient numerical method for the time‐fractional DPL model.

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New features of the fractional Euler-Lagrange equations for a physical system within non-singular derivative operator

Cited by 91 publications

References 34 publications

Stability analysis of a fractional-order SIS model on complex networks with linear treatment function

Stability analysis of a fractional-order SIS model on complex networks with linear treatment function

Filter regularization method for a time-fractional inverse advection–dispersion problem

Efficient and accurate spectral method for the time‐fractional dual‐phase‐lag heat transfer model and its parameter estimation

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