Optimal Control in Professional Gambling: A Fractional Logistic Dynamics Approach with Caputo-Fabrizio Derivatives

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Birla Institute of Technology and Science, Pilani, 333031 India.

2 Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati, 522237, India.

10.22034/cmde.2025.67868.3246

Abstract

The growing prevalence of excessive gambling has become a major concern in the 21st century, requiring urgent attention to mitigate its potential negative consequences. To address this problem, various preventive strategies, such as public awareness campaigns and educational programs, aim to highlight the detrimental effects of gambling addiction. Advanced mathematical modeling plays a pivotal role in promoting healthier behavior and preventing addiction-related problems. This article investigates a fractional-order mathematical model to understand gambling addiction across different user categories, including non-gamblers, exposed individuals, addicted gamblers, professional gamblers, and recovered gamblers. In the context of qualitative analysis, the study establishes the existence, uniqueness, nonnegativity, and boundedness of model solutions. Key elements of the fractional-order model are identified, including equilibrium points and the basic reproduction number. To assess the stability of the gambling addiction model in these user groups, the study applies the fractional Routh-Hurwitz criterion. Moreover, the global asymptotic stability of all equilibria is demonstrated through the construction of innovative Lyapunov functions. Numerical simulations and optimal control analysis of the fractional-order model further provide a detailed understanding of gambling addiction dynamics within these distinct user classes.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 20 April 2026

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History

  • Receive Date: 26 June 2025
  • Revise Date: 15 December 2025
  • Accept Date: 14 April 2026

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