King algorithm: A novel optimization approach based on variable-order fractional calculus with application in chaotic financial systems

Soradi‐Zeid, Samaneh; Jahanshahi, Hadi; Yousefpour, Amin; Bekiros, Stelios

doi:10.1016/j.chaos.2019.109569

Cited by 57 publications

(16 citation statements)

References 51 publications

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“…Fractional calculus is a subject in mathematical analysis, where it can be considered as a generalization of integer calculus [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Despite this, only in the past decades has it been extensively examined, owing to its broad range of use in many areas.…”

Section: Introductionmentioning

confidence: 99%

Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity

et al. 2022

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This research presents a new fractional-order discrete-time susceptible-infected-recovered (SIR) epidemic model with vaccination. The dynamical behavior of the suggested model is examined analytically and numerically. Through using phase attractors, bifurcation diagrams, maximum Lyapunov exponent and the 0−1 test, it is verified that the newly introduced fractional discrete SIR epidemic model vaccination with both commensurate and incommensurate fractional orders has chaotic behavior. The discrete fractional model gives more complex dynamics for incommensurate fractional orders compared to commensurate fractional orders. The reasonable range of commensurate fractional orders is between γ = 0.8712 and γ = 1, while the reasonable range of incommensurate fractional orders is between γ2 = 0.77 and γ2 = 1. Furthermore, the complexity analysis is performed using approximate entropy (ApEn) and C0 complexity to confirm the existence of chaos. Finally, simulations were carried out on MATLAB to verify the efficacy of the given findings.

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Section: Introductionmentioning

confidence: 99%

Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity

et al. 2022

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“…A mathematical model in non-singular order to investigate the coronavirus infection is considered in [28]. Nonetheless, some studies show that in some conditions, time-varying fractional-order models are able to better demonstrate behavior of systems [40][41][42][43][44][45][46][47]. However, now, there are few studies on time-varying fraction diseases dynamics, and it demands more studies in this field.…”

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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“…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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King algorithm: A novel optimization approach based on variable-order fractional calculus with application in chaotic financial systems

Cited by 57 publications

References 51 publications

Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity

Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity

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

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

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