Page 35 - IJOCTA-15-3

An International Journal of Optimization and Control: Theories & Applications
ISSN: 2146-0957 eISSN: 2146-5703
Vol.15, No.3, pp.407-425 (2025)
https://doi.org/10.36922/ijocta.7096

RESEARCH ARTICLE

Modeling and analysis of the dynamics of an excessive gambling
problem with modified fractional operator

4
1
Mulualem Aychluh , D.L. Suthar 2,3* , Clemente Cesarano , and S.D. Purohit 5
1
Department of Mathematics, Samara University, Samara, Afar, Ethiopia
2
Department of Mathematics, Wollo University, Dessie, Ethiopia
3
Department of Mathematics, Saveetha School of Engineering (SIMATS),Thandalam, Chennai,
Tamil Nadu, India
4
International Telematic University UNINETTUNO, Roma, Italy
5
Rajasthan Technical University, Kota, Rajasthan, India
muleaychluh62@gmail.com, dlsuthar@gmail.com, c.cesarano@uninettuno.it, sunil a purohit@yahoo.com
ARTICLE INFO ABSTRACT

Article History:
This work introduces a fractional-order model of gambling addiction using
Received: December 6, 2024
the modified Atangana-Baleanu-Caputo operator. We establish solution exis-
Revised: April 7, 2025
tence/uniqueness, derive the reproduction number R 0, and analyze stability.
Accepted: April 16, 2025
Published Online: May 5, 2025 Numerical results demonstrate how fractional order υ influences addiction dy-
namics. The model identifies key intervention parameters through sensitivity
Keywords: analysis. The optimal control strategy is proposed to reduce progression to ad-
Excessive gambling problem diction. These approaches provide new tools for understanding and managing
Modified fractional operator problem gambling behaviors.
Numerical method
Fractional mathematical modeling
AMS Classification 2010:
26A33; 34A08; 35H15; 34K50
47H10; 60H10

1. Introduction sophisticated casinos with slot machines, roulette
wheels, and poker tables. Technology has diversi-
Games of chance have a long history dating back fied gambling options, enabling various electronic
to Egyptian civilization. 1,2 Monetary rewards sig- video gambling activities. Many people benefit
nificantly contribute to popularity, as the primary from gambling, but many also incur unwanted
objective of gambling is to generate financial re- losses. This can lead to a difficult way of life, as
wards for lucky participants. These rewards en- individuals may try to spend more money to re-
hance the appeal of chance-based games and act cover from their losses. Every regular gambler en-
as psychological and biological factors in the de- counters what is known as a ”near-miss,” a failure
velopment of gambling addiction in many indi- that appears extremely close to success. This of-
viduals. Recently, gambling has grown into a ten leads to repeated gambling, ultimately trans-
rapidly expanding industry with millions of dol- forming gamblers into addicted ones. Surpris-
lars in cash flows. The world focus on gambling ingly, most games have the lowest probability of
has highlighted its uncontrolled distribution in winning. Anyone from any walk of life can lead to
modern society. There are several ways to gamble, gambling addiction. Several factors, including so-
ranging from state lotteries and sports betting cial, biological, and cognitive-educational aspects,
(including predicting football matches) to more may contribute to the progression from gambling
*Corresponding Author
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