Investigation of the hyperchaos and control in the fractional order financial system with profit margin

Johansyah, Muhamad Deni; Sambas, Aceng; Qureshi, Sania; Zheng, Song; Abed-Elhameed, Tarek M.; Vaidyanathan, Sundarapandian; Sulaiman, Ibrahim Mohammed

doi:10.1016/j.padiff.2023.100612

Cited by 14 publications

(2 citation statements)

References 37 publications

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“…See, for instance [2,15,36] and the references contained therein. For more sophisticated applications of dynamical systems studied using fractional calculus, we refer to [4,14,24,33].…”

Section: Introductionmentioning

confidence: 99%

On a class of piece-wise fractional order derivative delay differential equation with integral type condition

Shah,

Sher,

Sarwar

et al. 2024

J. Math. Computer Sci.

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In this paper, we present a detailed study of a class of fractional-order delay differential equations, highlighting that many real-world problems exhibit multifaceted behaviors in their dynamical interpretations. To capture the aforementioned behavior in a more realistic way, the use of piecewise derivatives of fractional orders has increasingly been applied. Given the significant role of delay differential equations in modeling various real-world scenarios, this work specifically addresses a type of delay differential equation with a proportional delay term. Employing piecewise fractional derivatives and Ulam-Hyers (U-H) type stability analysis, we explore the qualitative theory of the analyzed problem. Utilizing fixed-point theory and techniques from functional analysis, we aim to achieve the desired outcomes. To demonstrate our findings, several illustrative examples are provided.

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“…See, for instance [2,15,36] and the references contained therein. For more sophisticated applications of dynamical systems studied using fractional calculus, we refer to [4,14,24,33].…”

Section: Introductionmentioning

confidence: 99%

On a class of piece-wise fractional order derivative delay differential equation with integral type condition

Shah,

Sher,

Sarwar

et al. 2024

J. Math. Computer Sci.

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show abstract

“…For instance, researchers [34] have studied SARS-CoV-2 by using a mathematical model. Financial models and a prey-predator system were studied by applying mathematical formulations by researchers [23] and [35]. In the same way, a COVID-19 mathematical model was investigated by researchers [47].…”

mentioning

confidence: 99%

On mathematical model of infectious disease by using fractals fractional analysis

Eiman,

Shah,

Sarwar

et al. 2024

DCDS-S

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Here, we remarked that fractals or Housdarff derivatives are important tools to investigate various problems. However, fractals when combined with fractional orders of different kernels give birth to a big class of operators. Each operator has its own importance and applicability. One of the fractals-fractional operators is based on the exponential kernel which has also many important uses in modeling of different real-world problems. Reinfection is a worldwide issue nowadays and due to reinfection, people in our society are facing a lot of issues like economical, social, and a high rate of death. A fractal-fractional hybrid model with reinfection was investigated. The mentioned model was considered to deduce the qualitative theory and numerical aspects. Fundamental properties of the mentioned model were deduced including basic reproduction number, equilibrium points, and global and local stability of both equilibrium points. The qualitative analysis was consisted on the existence and stability in sense of Hyers-Ulam of the solutions. Interpolation technique was used to deduce a numerical scheme for the model under our study. Additionally, criteria for uniqueness of solution was proved by the Banach principle. In addition, sensitivity analysis was also included in the paper. Various numerical results were presented using different values of fractals fractional order. Some comparisons of simulated and real data was also given.

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A novel design of recurrent neural network to investigate the heat transmission of radiative Casson nanofluid flow consisting of carbon nanotubes (CNTs) across a curved stretchable surface

Shahbaz,

Ahmad,

Raja

et al. 2024

Z Angew Math Mech

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This study aims to develop a supervised learning artificial recurrent neural network algorithm supported by Bayesian regularization called (ARNN‐BR) to analyze the impact of physical parameters, including radius of curvature (), Casson parameter (), heat generation parameter () and radiation parameter () on velocity fʹ(η), and temperature profiles θ(η) in Casson nanofluid consisting of carbon nanotubes (CNTs‐CNF) model for single and multiwalled CNTs across a curved stretched surface. The numerical dataset of the proposed model has been constructed by varying various parameters for five scenarios that are used in a Bayesian regularization‐based intelligent computing method to build networks for approximating the numerical solutions of CNTs‐CNF model. It is observed that increment in the dimensionless radius of curvature () causes to rise an increase in the velocity profile fʹ(η) for both SWCNTs and MWCNTs. However, a contrasting trend is observed when the Casson parameter () is increased to higher values. The temperature θ(η) of fluid increases as the heat generation parameter () and radiation parameter () increase. However, an opposite behavior is noticed when the dimensionless radius of curvature () varies. The effectiveness and significance of designed Bayesian regularization based artificial recurrent neural networks (ARNN‐BR) is demonstrated through regression index measurements, error histogram studies, auto‐correlation analysis and convergence curves showing a minimal level of mean square error (E‐11 to E‐04) for the comprehensive simulations of CNTs‐CNF model. The designed ARNN‐BR algorithm is employed in many domains such as voice recognition, machine translation, identification of neurological brain illnesses as well as for automated translation of texts across different languages.

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Investigation of the hyperchaos and control in the fractional order financial system with profit margin

Cited by 14 publications

References 37 publications

On a class of piece-wise fractional order derivative delay differential equation with integral type condition

On a class of piece-wise fractional order derivative delay differential equation with integral type condition

On mathematical model of infectious disease by using fractals fractional analysis

A novel design of recurrent neural network to investigate the heat transmission of radiative Casson nanofluid flow consisting of carbon nanotubes (CNTs) across a curved stretchable surface

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