scholarly journals Signal Smoothing with Time-Space Fractional Order Model

2021 ◽  
Vol 21 (1) ◽  
pp. 25-32
Author(s):  
Yuanlu Li
Keyword(s):  
Diffusion Model ◽  
Fractional Order ◽  
Order Model ◽  
Comparison Result ◽  
Smoothing Methods ◽  
Fractional Order Model ◽  
Time Space ◽  
Proposed Model ◽  
Noisy Signals ◽  
And Performance

Abstract The time-space fractional-order model (TSFOM) is a generation of the classical diffusion model which is an excellent smoothing method. In this paper, the fractional-order derivative in the model is found to have good performance for peak-preserving. To check the validity and performance of the model, some noisy signals are smoothed by some commonly used smoothing methods and results are compared with those of the proposed model. The comparison result shows that the proposed method outperforms the classical nonlinear diffusion model and some commonly used smoothing methods.

scholarly journals Dynamical analysis of fractional-order of IVGTT glucose–insulin interaction

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mansoor H. Alshehri ◽  
Sayed Saber ◽  
Faisal Z. Duraihem
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Euler Method ◽  
Dynamical Analysis ◽  
Order Model ◽  
Insulin Metabolism ◽  
Fractional Order Model ◽  
Proposed Model ◽  
Predictor Corrector ◽  
Tolerance Testing

Abstract This paper proposes a fractional-order model of glucose–insulin interaction. In Caputo’s meaning, the fractional derivative is defined. This model arises in Bergman’s minimal model, used to describe blood glucose and insulin metabolism, after intravenous tolerance testing. We showed that the established model has existence, uniqueness, non-negativity, and boundedness of fractional-order model solutions. The model’s local and global stability was investigated. The parametric conditions under which a Hopf bifurcation occurs in the positive steady state for a proposed model are studied. Moreover, we present a numerical treatment for solving the proposed fractional model using the generalized Euler method (GEM). The model’s local stability and Hopf bifurcation of the proposed model in sense of the GEM are presented. Finally, numerical simulations of the model using the Adam–Bashforth–Moulton predictor corrector scheme and the GEM have been presented to support our analytical results.

scholarly journals Fractional Order Model of the Two Dimensional Heat Transfer Process

Energies ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 6371
Author(s):  
Krzysztof Oprzędkiewicz ◽  
Wojciech Mitkowski ◽  
Maciej Rosół
Keyword(s):  
Heat Transfer ◽  
Fractional Order ◽  
Heat Transfer Process ◽  
Two Dimensional ◽  
Thermal Camera ◽  
Order Model ◽  
Fractional Order Model ◽  
Proposed Model ◽  
Spectrum Decomposition ◽  
Theoretical Results

In this paper, a new, state space, fractional order model of a heat transfer in two dimensional plate is addressed. The proposed model derives directly from a two dimensional heat transfer equation. It employes the Caputo operator to express the fractional order differences along time. The spectrum decomposition and stability of the model are analysed. The formulae of impluse and step responses of the model are proved. Theoretical results are verified using experimental data from thermal camera. Comparison model vs experiment shows that the proposed fractional model is more accurate in the sense of MSE cost function than integer order model.

scholarly journals A fractional-order model describing the dynamics of the novel coronavirus (COVID-19) with nonsingular kernel

2021 ◽  
Vol 146 ◽  
pp. 110859
Author(s):  
Ahmed Boudaoui ◽  
Yacine El hadj Moussa ◽  
Zakia Hammouch ◽  
Saif Ullah
Keyword(s):  
Fractional Order ◽  
The Novel ◽  
Order Model ◽  
Fractional Order Model ◽  
Novel Coronavirus

Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems

2017 ◽  
Vol 6 (2) ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Anitha Karthikeyan ◽  
Prakash Duraisamy
Keyword(s):  
Permanent Magnet ◽  
Fractional Order ◽  
Dynamic Properties ◽  
Synchronous Generator ◽  
Adaptive Controller ◽  
Control Technique ◽  
Order Model ◽  
Permanent Magnet Synchronous Generator ◽  
Chaos Suppression ◽  
Fractional Order Model

AbstractIn this paper we investigate the control of three-dimensional non-autonomous fractional-order uncertain model of a permanent magnet synchronous generator (PMSG) via a adaptive control technique. We derive a dimensionless fractional order model of the PMSM from the integer order presented in the literatures. Various dynamic properties of the fractional order model like eigen values, Lyapunov exponents, bifurcation and bicoherence are investigated. The system chaotic behavior for various orders of fractional calculus are presented. An adaptive controller is derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the robust controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results derived through which we show that for the derived adaptive controller and the parameter update law, the origin of the system for any bounded initial conditions is asymptotically stable.

scholarly journals Identification of a PEMFC fractional order model

2017 ◽  
Vol 42 (2) ◽  
pp. 1499-1509 ◽  
Author(s):  
Miassa Amira Taleb ◽  
Olivier Béthoux ◽  
Emmanuel Godoy
Keyword(s):  
Fractional Order ◽  
Order Model ◽  
Fractional Order Model
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