Optimal Control of Time-Delay Fractional Equations via a Joint Application of Radial Basis Functions and Collocation Method

Chen, Shubo; Soradi-Zeid, Samaneh; Jahanshahi, Hadi; Alcaraz, Raúl; Gómez-Aguilar, J. F.; Bekiros, Stelios; Chu, Yu‐Ming

doi:10.3390/e22111213

Cited by 55 publications

(16 citation statements)

References 48 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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“…The fractional order derivatives gain considerable attention and widely used in the formulation of epidemic modeling are Caputo [11] , Caputo–Fabrizio [12] and Atangana-Baleanu-Caputo (ABC) [13] . The application of various fractional order operator depending on singular and non-singular kernels are describes in the recent literature such as [14] , [15] , [16] , [17] . The fractional operators have been used widely to address the complex dynamics and possible control of COVID-19, one of the recent key challenges to humans around the globe.…”

Section: Introductionmentioning

confidence: 99%

Modeling the dynamics of coronavirus with super-spreader class: A fractal-fractional approach

et al. 2022

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Super-spreaders of the novel coronavirus disease (or COVID-19) are those with greater potential for disease transmission to infect other people. Understanding and isolating the super-spreaders are important for controlling the COVID-19 incidence as well as future infectious disease outbreaks. Many scientific evidences can be found in the literate on reporting and impact of super-spreaders and super-spreading events on the COVID-19 dynamics. This paper deals with the formulation and simulation of a new epidemic model addressing the dynamics of COVID-19 with the presence of super-spreader individuals. In the first step, we formulate the model using classical integer order nonlinear differential system composed of six equations. The individuals responsible for the disease transmission are further categorized into three sub-classes, i.e., the symptomatic, super-spreader and asymptomatic. The model is parameterized using the actual infected cases reported in the kingdom of Saudi Arabia in order to enhance the biological suitability of the study. Moreover, to analyze the impact of memory index, we extend the model to fractional case using the well-known Caputo–Fabrizio derivative. By making use of the Picard-Lindelöf theorem and fixed point approach, we establish the existence and uniqueness criteria for the fractional-order model. Furthermore, we applied the novel fractal-fractional operator in Caputo–Fabrizio sense to obtain a more generalized model. Finally, to simulate the models in both fractional and fractal-fractional cases, efficient iterative schemes are utilized in order to present the impact of the fractional and fractal orders coupled with the key parameters (including transmission rate due to super-spreaders) on the pandemic peaks.

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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

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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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Optimal Control of Time-Delay Fractional Equations via a Joint Application of Radial Basis Functions and Collocation Method

Cited by 55 publications

References 48 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

Modeling the dynamics of coronavirus with super-spreader class: A fractal-fractional approach

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

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