Coexisting attractors in a fractional order hydro turbine governing system and fuzzy PID based chaos control

Rajagopal, Karthikeyan; Jahanshahi, Hadi; Jafari, Sajad; Weldegiorgis, Riessom; Duraisamy, Prakash

doi:10.1002/asjc.2261

Cited by 34 publications

(12 citation statements)

References 53 publications

(57 reference statements)

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“…Moreover, the authors in [18][19][20][21][22] considered the COVID-19 infection models in fractional derivatives and some recommendations regarding the minimization of infection are given in the form of lockdown and control strategies. Moreover, the applications of fractional calculus and the numerical methods for the physical and biological problems have been discussed in [23][24][25][26][29][30][31][32][33][34][35][36][37][38][39]. For example, the HIV infection model with antiviral drug therapy is considered in [23].…”

Section: Introductionmentioning

confidence: 99%

A mathematical model for SARS-CoV-2 in variable-order fractional derivative

DarAssi

Safi

Khan

et al. 2022

Eur. Phys. J. Spec. Top.

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A new coronavirus mathematical with hospitalization is considered with the consideration of the real cases from March 06, 2021 till the end of April 30, 2021. The essential mathematical results for the model are presented. We show the model stability when in the absence of infection. We show that the system is stable locally asymptotically when at infection free state. We also show that the system is globally asymptotically stable in the disease absence when . Data have been used to fit accurately to the model and found the estimated basic reproduction number to be . Some graphical results for the effective parameters are drawn for the disease elimination. In addition, a variable-order model is introduced, and so as to handle the outbreak effectively and efficiently, a genetic algorithm is used to produce high-quality control. Numerical simulations clearly show that decision-makers may develop helpful and practical strategies to manage future waves by implementing optimum policies.

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Section: Introductionmentioning

confidence: 99%

A mathematical model for SARS-CoV-2 in variable-order fractional derivative

DarAssi

Safi

Khan

et al. 2022

Eur. Phys. J. Spec. Top.

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“…Despite the long history of fractional calculus, its applications are only a new subject of interest. Fractional calculus has recently been utilized in various fields of study [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ]. Also, the modeling of HIV using fractional differential equations has started to attract some research attention.…”

Section: Introductionmentioning

confidence: 99%

A Caputo–Fabrizio Fractional-Order Model of HIV/AIDS with a Treatment Compartment: Sensitivity Analysis and Optimal Control Strategies

Wang

Jahanshahi

Wang

et al. 2021

Entropy

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Although most of the early research studies on fractional-order systems were based on the Caputo or Riemann–Liouville fractional-order derivatives, it has recently been proven that these methods have some drawbacks. For instance, kernels of these methods have a singularity that occurs at the endpoint of an interval of definition. Thus, to overcome this issue, several new definitions of fractional derivatives have been introduced. The Caputo–Fabrizio fractional order is one of these nonsingular definitions. This paper is concerned with the analyses and design of an optimal control strategy for a Caputo–Fabrizio fractional-order model of the HIV/AIDS epidemic. The Caputo–Fabrizio fractional-order model of HIV/AIDS is considered to prevent the singularity problem, which is a real concern in the modeling of real-world systems and phenomena. Firstly, in order to find out how the population of each compartment can be controlled, sensitivity analyses were conducted. Based on the sensitivity analyses, the most effective agents in disease transmission and prevalence were selected as control inputs. In this way, a modified Caputo–Fabrizio fractional-order model of the HIV/AIDS epidemic is proposed. By changing the contact rate of susceptible and infectious people, the atraumatic restorative treatment rate of the treated compartment individuals, and the sexual habits of susceptible people, optimal control was designed. Lastly, simulation results that demonstrate the appropriate performance of the Caputo–Fabrizio fractional-order model and proposed control scheme are illustrated.

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“…On the other hand, some chaotic models, found in theoretical research, can also be widely used in practical problems. To date, many control techniques, including backstepping method [Yassen, 2007], adaptive control [12,13,29,35], fuzzy control [10,20,27,28], optimal control [32], and sliding mode control (SMC) [9][10][11] have been proposed for nonlinear and chaotic system. SMC as a robust control technique has attracted remarkable attention in various practical applications [37].…”

Section: Introductionmentioning

confidence: 99%