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1

A robust study of the transmission dynamics of zoonotic infection through non-integer derivative

Jan Rashid, Alharbi Asma, Boulaaras Salah, Alyobi Sultan, Khan Zaryab

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

922--938

EN

In Sub-Saharan Africa, zoonotic diseases are the leading cause of sickness and mortality, yet preventing their spread has long been difficult. Vaccination initiatives have significantly reduced the frequency of zoonotic diseases mostly in African regions. Nonetheless, zoonotic illnesses continue to be a hazard to underdeveloped countries. Zoonotic infections are spread by direct contact, food, and water. We construct an epidemic model to understand zoonotic disease transmission phenomena. The model is examined using the fundamental results of fractional theory. The reproduction parameter R0 was obtained by inspecting the model’s steady states. The stability of the system’s steady states has been demonstrated. The system’s reproduction parameter is quantitatively explored by varying various input parameters. Furthermore, the presence and uniqueness of the solution of the proposed dynamics of zoonotic diseases have been demonstrated. Different simulations of the recommended zoonotic disease model with different input factors are performed to inspect the complex dynamics of zoonotic disease with the influence of various model factors. To establish effective prevention and control measures for the infection, we analyse dynamical behaviour of the system. Decreasing the fractional order θ can decrease the infection level significantly. Different factors for reducing zoonotic diseases were recommended to regional policymakers.

2

A numerical study of anomalous electro-diffusion cells in cable sense with a non-singular kernel

Iqbal Azhar, Akram Tayyaba

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

574--586

EN

The time-fractional cable model is solved using an extended cubic B-spline (ECBS) collocation strategy. The B-spline function was used for space partitioning, while the Caputo-Fabrizio (CF) was used for temporal discretization. The finite difference technique was used to discretize the CF operator. For the first time in cable modeling, the CF operator has been used. In terms of time, the convergence of order τ . An ECBS collocation approach is investigated by numerical example at different values, and comparisons with published work are made. The numerical results show that the scheme performed well, and the graphical representations show that the results are very close to exact values. The Von Neumann technique is applied to investigate the stability of the proposed scheme.

3

Analysis of Caputo-Fabrizio operator application for synthesis of fractional order PID-controller

Lozynskyy Andriy, Lozynskyy Orest., Kasha Lidiya, Holovach Ihor

Przegląd Elektrotechniczny

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2021

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R. 97, nr 6

66--71

EN

Using the representation of Caputo and Fabrizio, the influence of substitution in the linear model of a two-mass system of integer derivatives on fractional order derivatives is shown in this paper. So, the change of parameters of PID-controller of fractional order in comparison with classical PID-controller is analyzed. The influence of the use of PID-controller of fractional order on the transient characteristics of the system is demonstrated in the results of this paper.

PL

Korzystając z reprezentacji Caputo i Fabrizio, ukazano wpływ zastąpienia pochodnych całkowitego rzędu w liniowym, modelu układu dwóch mas, pochodnymi ułamkowego rzędu. Przeanalizowano zmianę parametrów regulatora PID ułamkowego rzędu względem klasycznego regulatora PID. Zademonstrowano wyniki przedstawiające wpływ wykorzystania regulatora PID ułamkowego rzędu na charakterystykę przejściową układu.

4

The Caputo vs. Caputo-Fabrizio operators in modeling of heat transfer process

Oprzędkiewicz K., Mitkowski W., Gawin E., Dziedzic K.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2018

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Vol. 66, nr 4

501--507

EN

In the paper two non-integer order, state space models of heat transfer process are compared. The first uses a known Caputo operator and the second – a new operator proposed by Caputo and Fabrizio in 2015. Both discussed models are modifications of a known, integer order, state space, semigroup model of heat transfer process. Parameters of both models were identified by means of optimization of MSE cost function with the use of simplex method, available in MATLAB. Both proposed models have been compared in the aspect of accuracy and convergence. Analytical and numerical results show that the Caputo-Fabrizio model is faster convergent and easier to implement than the Caputo model. However, its accuracy in the sense of MSE cost function is worse.

5

Non integer order, state space model of heat transfer process using Caputo-Fabrizio operator

Oprzędkiewicz K.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2018

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Vol. 66, nr 3

249--255

EN

The paper is intended to show a new state space, non integer order model of an one-dimensional heat transfer process. The proposed model derives directly from time continuous, state space semigroup model. The fractional order derivative with respect to time is by a new operator proposed by Caputo and Fabrizio, the non integer order spatial derivative is expressed by Riesz operator. The Caputo-Fabrizio operator can be directly implementated using MATLAB, because it does not require us to apply any approximation. Analytical formulae of step response are given, the system decomposition was discussed also. Main results from the paper show that the use of Caputo Fabrizio operator allows us to obtain the simple in implementation and analysis model of the considered heat transfer process. The accuracy of the proposed model in the sense of a MSE cost function is satisfying.