The effect of market confidence on a financial system from the perspective of fractional calculus: Numerical investigation and circuit realization

Chen, Shubo; Jahanshahi, Hadi; Abba, Oumate Alhadji; Solís-Pérez, J.E.; Bekiros, Stelios; Gómez‐Aguilar, J.F.; Yousefpour, Amin; Chu, Yu‐Ming

doi:10.1016/j.chaos.2020.110223

Cited by 119 publications

(26 citation statements)

References 34 publications

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“…In (2) the initial value of the level or stock variable known as Inventory is established, in (3) the equation of the exchange rate or flow known as Reception is established and in (4) the equation of the outflow is established known as Delivery; This initial value and these two equations are key for the Inventory level variable since to know the value of the Inventory variable that represents the "state of the system's inventory", it is necessary to know both the initial value of the Inventory as well as the equations of the flows that are "connected" to the Inventory variable.…”

Section: Mathematical Equationsmentioning

confidence: 99%

“…This system dynamics model [2] can show different states of difficulty, therefore, it is convenient to know well what you want to analyze, for which we have to select the topic (It has to be oriented to the problem that you want to address), identify the variables, determine the limit (In the future how far we want to go in the behavior of the system and in the past to know what were the ultimate causes that originated the irregular behavior), build the causal diagram (To observe the relationships of the variables), construct the Forrester diagram and finally enter the equations so that a correct analysis can be carried out that gives us the ability to have a clear idea of the system in question [3].…”

Section: Introductionmentioning

confidence: 99%

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Inventory Management Analysis under the System Dynamics Model

Morales¹,

Andrade–Arenas²

2021

IJACSA

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In this work, the modeling of the system dynamics concerning inventory management has been carried out, this was done to achieve a correct analysis on said management, and thus make decisions that benefit the company. Knowing that the problem lies in the mismanagement of inventories, which are managed by certain companies with little or vast knowledge about inventory management, for which, it is desired to make use of the system dynamics modeling, so that this, achieves a correct analysis of the management, but is focused on the dynamics of system. The result obtained, from the development of the methodology applied in this work, was a correct and adequate analysis of the dynamics modeling of system in inventory management, which was achieved, using the simulation software known as Vensim, and a methodology based on three stages that are the Causal Diagram, the Forrester Diagram, and the mathematical equations.

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Section: Mathematical Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Inventory Management Analysis under the System Dynamics Model

Morales¹,

Andrade–Arenas²

2021

IJACSA

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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

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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The effect of market confidence on a financial system from the perspective of fractional calculus: Numerical investigation and circuit realization

Cited by 119 publications

References 34 publications

Inventory Management Analysis under the System Dynamics Model

Inventory Management Analysis under the System Dynamics Model

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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