Structure Preserving Algorithm for Fractional Order Mathematical Model of COVID-19

Purpose The present work is concerned with the solution of a fractional-order thermoelastic problem of a two-dimensional infinite half space under axisymmetric distributions in which lower surface is traction free and subjected to a periodically varying heat source. The thermoelastic displacement, stresses and temperature are determined within the context of fractional-order thermoelastic theory. To observe the variations of displacement, temperature and stress inside the half space, the authors compute the numerical values of the field variables for copper material by utilizing Gaver-Stehfast algorithm for numerical inversion of Laplace transform. The effects of fractional-order parameter on the variations of field variables inside the medium are analyzed graphically. The paper aims to discuss these issues. Design/methodology/approach Integral transform technique and Gaver-Stehfast algorithm are applied to prepare the mathematical model by considering the periodically varying heat source in cylindrical co-ordinates. Findings This paper studies a problem on thermoelastic interactions in an isotropic and homogeneous elastic medium under fractional-order theory of thermoelasticity proposed by Sherief (Ezzat and El-Karamany, 2011b). The analytic solutions are found in Laplace transform domain. Gaver-Stehfast algorithm (Ezzat and El-Karamany, 2011d; Ezzat, 2012; Ezzat, El Karamany, Ezzat, 2012) is used for numerical inversion of the Laplace transform. All the integrals were evaluated using Romberg’s integration technique (El-Karamany et al., 2011) with variable step size. A mathematical model is prepared for copper material and the results are presented graphically with the discussion on the effects of fractional-order parameter. Research limitations/implications Constructed purely on theoretical mathematical model by considering different parameters and the functions. Practical implications The system of equations in this paper may prove to be useful in studying the thermal characteristics of various bodies in real-life engineering problems by considering the time fractional derivative in the field equations. Originality/value In this problem, the authors have used the time fractional-order theory of thermoelasticity to solve the problem for a half space with a periodically varying heat source to control the speed of wave propagation in terms of heat and elastic waves for different conductivity like weak conductivity, moderate conductivity and super conductivity which is a new and novel contribution.

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Fractional-Order Modelling and Optimal Control of Cholera Transmission

Fractal and Fractional ◽

10.3390/fractalfract5040261 ◽

2021 ◽

Vol 5 (4) ◽

pp. 261

Author(s):

Silvério Rosa ◽

Delfim F. M. Torres

Keyword(s):

Mathematical Model ◽

Optimal Control ◽

Sensitivity Analysis ◽

Fractional Order ◽

Control Measures ◽

Time Interval ◽

Variable Order ◽

Effectiveness Analysis ◽

The Cost ◽

Derivative Order

A Caputo-type fractional-order mathematical model for “metapopulation cholera transmission” was recently proposed in [Chaos Solitons Fractals 117 (2018), 37–49]. A sensitivity analysis of that model is done here to show the accuracy relevance of parameter estimation. Then, a fractional optimal control (FOC) problem is formulated and numerically solved. A cost-effectiveness analysis is performed to assess the relevance of studied control measures. Moreover, such analysis allows us to assess the cost and effectiveness of the control measures during intervention. We conclude that the FOC system is more effective only in part of the time interval. For this reason, we propose a system where the derivative order varies along the time interval, being fractional or classical when more advantageous. Such variable-order fractional model, that we call a FractInt system, shows to be the most effective in the control of the disease.

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Fractional-Order Modeling and Simulation of Magnetic Coupled Boost Converter in Continuous Conduction Mode

International Journal of Bifurcation and Chaos ◽

10.1142/s021812741850061x ◽

2018 ◽

Vol 28 (05) ◽

pp. 1850061 ◽

Cited By ~ 5

Author(s):

Zirui Jia ◽

Chongxin Liu

Keyword(s):

Mathematical Model ◽

Mathematical Models ◽

Fractional Order ◽

Transfer Functions ◽

Circuit Simulation ◽

Boost Converter ◽

Averaged Model ◽

Conduction Mode ◽

State Average ◽

Continuous Conduction Mode

By using fractional-order calculus theory and considering the condition that capacitor and inductor are naturally fractional, we construct the fractional mathematical model of the magnetic coupled boost converter with tapped-inductor in the operation of continuous conduction mode (CCM). The fractional state average model of the magnetic coupled boost converter in CCM operation is built by exploiting state average modeling method. In these models, the effects of coupling factor, which is viewed as one generally, are directly pointed out. The DC component, the AC component, the transfer functions and the requirements of the magnetic coupled boost converter in CCM operation are obtained and investigated on the basis of the state averaged model as well as its fractional mathematical model. Using the modified Oustaloup’s method for filter approximation algorithm, the derived models are simulated and compared using Matlab/Simulink. In order to further verify the fractional model, circuit simulation is implemented. Furthermore, the differences between the fractional-order mathematical models and the corresponding integer-order mathematical models are researched. Results of the model and circuit simulations validate the effectiveness of theoretical analysis.

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Mathematical Model for Hyperbolic Two Temperature Fractional-Order Thermoelastic Materials Subjected to Thermal Loading

Applied Mathematics & Information Sciences ◽

10.18576/amis/150104 ◽

2021 ◽

Vol 15 (1) ◽

pp. 23-29

Keyword(s):

Mathematical Model ◽

Fractional Order ◽

Thermal Loading ◽

Two Temperature

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An active control for hydrostatic journal bearing using optimization algorithms

Industrial Lubrication and Tribology ◽

10.1108/ilt-07-2020-0272 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Waheed Ur Rehman ◽

Xinhua Wang ◽

Yingchun Chen ◽

Xiaogao Yang ◽

Zia Ullah ◽

...

Keyword(s):

Mathematical Model ◽

Peer Review ◽

Fractional Order ◽

Journal Bearing ◽

Optimization Techniques ◽

Performance Criteria ◽

Content Type ◽

Control Techniques ◽

Fractional Order Controller ◽

Fractional Order Pid

Purpose The purpose of this paper is to improve static/dynamic characteristics of active-controlled hydrostatic journal bearing by using fractional order control techniques and optimizing algorithms. Design/methodology/approach Active lubrication has ability to overcome the unpredictable harsh environmental conditions which often lead to failure of capillary controlled traditional hydrostatic journal bearing. The research develops a mathematical model for a servo feedback-controlled hydrostatic journal bearing and dynamics of model is analyzed with different control techniques. The fractional-order PID control system is tuned by using particle swarm optimization and Nelder mead optimization techniques with the help of using multi-objective performance criteria. Findings The results of the current research are compared with previously published theoretical and experimental results. The proposed servo-controlled active bearing system is studied under a number of different dynamic situations and constraints of variable spindle speed, external load, temperature changes (viscosity) and variable bearing clearance (oil film thickness). The simulation results show that the proposed system has better performance in terms of controllability, faster response, stability, high stiffness and strong resistance. Originality/value This paper develops an accurate mathematical model for servo-controlled hydrostatic bearing with fractional order controller. The results are in excellent agreement with previously published literature. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2020-0272

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FRACTIONAL ORDER ANALYSIS OF HBV AND HCV CO-INFECTION UNDER ABC DERIVATIVE

Fractals ◽

10.1142/s0218348x22400369 ◽

2021 ◽

Author(s):

HUSSAM ALRABAIAH ◽

MATI UR RAHMAN ◽

IBRAHIM MAHARIQ ◽

SAMIA BUSHNAQ ◽

MUHAMMAD ARFAN

Keyword(s):

Mathematical Model ◽

Fixed Point ◽

Approximate Solution ◽

Fractional Order ◽

Fixed Point Theory ◽

Point Theory ◽

Comparative Result ◽

Order Analysis ◽

The Stability ◽

Fractional Orders

In this paper, we consider a fractional mathematical model describing the co-infection of HBV and HCV under the non-singular Mittag-Leffler derivative. We also investigate the qualitative analysis for at least one solution and a unique solution by applying the approach fixed point theory. For an approximate solution, the technique of the iterative fractional order Adams–Bashforth scheme has been implemented. The simulation for the proposed scheme has been drawn at various fractional order values lying between (0,1) and integer-order of 1 via using Matlab. All the compartments have shown convergence and stability with time. A detailed comparative result has been given by the different fractional orders, which showed that the stability was achieved more rapidly at low orders.

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