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1

Generalized thermoelastic heat conduction model involving three different fractional operators

Saidi Anouar, Yahya Ahmed M. H, Abouelregal Ahmed E., Dargail Husam E., Ahmed Ibrahim-Elkhalil, Ali Elsiddeg, Mohammed F. A.

Advances in Materials Science

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2023

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Vol. 23, nr 2(76)

25--44

EN

The purpose of this paper is to introduce a new time-fractional heat conduction model with three-phase-lags and three distinct fractional-order derivatives. We investigate the introduced model in the situation of an isotropic and homogeneous solid sphere. The exterior of the sphere is exposed to a thermal shock and a decaying heat generation rate. We recuperate some earlier thermoelasticity models as particular cases from the proposed model. Moreover, the effects of different fractional thermoelastic models and the effect of instant time on the physical variables of the medium are studied. We obtain the numerical solutions for the various physical fields using a numerical Laplace inversion technique. We represent the obtained results graphically and discuss them. Physical views presented in this article may be useful for the design of new materials, bio-heat transfer mechanisms between tissues and other scientific domains.

2

A single image deblurring approach based on a fractional order dark channel prior

Yu Xiaoyuan, Xie Wei, Yu Jinwei

International Journal of Applied Mathematics and Computer Science

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2022

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Vol. 32, no. 3

441--454

EN

The dark channel prior has been successfully applied to solve the blind deblurring problem on different scene images. Since the dark channel of the blurry-noise image is similar to that of the corresponding clear image, the sparsity of the dark channel is less effective for image blind deblurring. Inspired by the fact that a fractional order calculation can inhibit the noise and preserve the texture information of the image, a fractional order dark channel prior is proposed for image deblurring in this paper. It is appropriate for kernel estimation where input images and intermediate images are processed by using a fractional order dark channel prior. Furthermore, the non-convex problem is solved by the half-quadratic splitting method, and some metrics are used for deblurring image quality assessment. Finally, quantitative and qualitative experimental results show that the proposed method achieves state-of-the-art results on synthetic and real blurry images.

3

Synchronization of fractional-order discrete-time chaotic systems by an exact delayed state reconstructor: Application to secure communication

Djennoune Said, Bettayeb Maamar, Al-Saggaf Ubaid Muhsen

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 1

179--194

EN

This paper deals with the synchronization of fractional-order chaotic discrete-time systems. First, some new concepts regarding the output-memory observability of non-linear fractional-order discrete-time systems are developed. A rank criterion for output-memory observability is derived. Second, a dead-beat observer which recovers exactly the true state system from the knowledge of a finite number of delayed inputs and delayed outputs is proposed. The case of the presence of an unknown input is also studied. Third, secure data communication based on a generalized fractional-order Hénon map is proposed. Numerical simulations and application to secure speech communication are presented to show the efficiency of the proposed approach.

4

Fractional-order feedback control of a pneumatic servo-drive

Laski P. A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2019

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Vol. 67, nr 1

53--59

EN

A fractional-order control strategy for a pneumatic position servo-system is presented in this paper. The idea of the fractional calculus application to control theory was introduced in many works, and its advantages were proved. This paper deals with the design of fractional order PIλDμ controllers, in which the orders of the integral and derivative parts, λ and μ, respectively, are fractional. Experiments with fractionalorder controller are performed under various conditions, which include position signal with different frequencies and amplitudes or a step position signal. The results show the effectiveness of the proposed schemes and verify their fine control performance for a pneumatic position servo-system.

5

Zastosowanie rachunku różniczkowego ułamkowego rzędu do modelowania dynamiki superkondensatorów

Orzyłowski M., Lewandowski M.

Przegląd Elektrotechniczny

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2014

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R. 90, nr 8

13-17

PL

Artykuł omawia modelowanie impedancji superkondsnsatorów przy zastosowaniu rachunku różniczkowo-całkowym ułamkowych rzędów oraz modelu relaksacji dielektrycznej Cole’a-Cole’a. Podstawą modelowania są zidentyfikowane charakterystyki częstotliwościowe. Modelowaniu ułamkowego rzędu przeciwstawia modelowanie z zastosowaniem transmitancji rzędu całkowitego. Prezentuje dokładność obu metod modelowania oraz trudności obliczeniowe podczas optymalizacji wartości parametrów modeli, a także aplikację tych modeli do celów sterowania.

EN

The paper describes the modeling of supercapacitor impedance with fractional order calculus and Cole-Cole relaxation model application. The basis of the modeling are frequency responses. The fractional order models are compared with integer order transfer functions. The accuracy of both methods of modeling and difficulties of the optimization of parameters values of the models are discussed. The applications of both types of transfer function in control circuits are presented.

6

Design of Fractional Order Sliding Mode Controller Based on Parameters Tuning

Zhang B., Pi Y.

Przegląd Elektrotechniczny

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2012

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R. 88, nr 10a

172-175

EN

For dealing with the chattering phenomenon existing in conventional first order sliding mode controller, in this paper, a fractional order sliding mode controller (FOSMC) is proposed. Based on the advantage of fractional order differential and integral calculus, the sliding mode surface is designed with fractional order differential but not integral order. Under the stable performance of system, the parameters of sliding mode surface are tuned by given crossover frequency and phase margin. Furthermore, the soft-switching gain is obtained used fuzzy logic inference system. Simulations and experiments demonstrate that the proposed fractional order sliding mode controller not only achieve high control performance, but also is robust with regard to external disturbance.

PL

W artykule zaproponowano ułamkowy sterownik ślizgowy FOSMC. Przy ustalonych parametrach systemu powierzchnia ślizgowa jest dobierana przez uwzględnianie częstotliwości i marginesu fazy. Przełączane wzmocnienie jest realizowane po zastosowaniu układu logiki rozmytej. Układ jest bardziej odporny na zewnętrzne zakłócenia. (Projekt sterownika ślizgowego ułamkowego rzędu bazujący na dobieraniu parametrów)