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M. Aychluh et.al. / IJOCTA, Vol.15, No.3, pp.407-425 (2025)
to problem gambling, which is a form of addic- et al. 14 The authors of Michalczuk et al. 15 stud-
tion. Problem gambling reflects a loss of control ied pathological gamblers’ impulsivity and cog-
over gambling that persists despite often severe nitive distortions at the United Kingdom’s na-
negative consequences. 3 tional problem gambling clinic. Sharpe et al. 16
formulated a cognitive-behavioral model of prob-
Gambling addiction occurs when gambling lem gambling from a biopsychosocial perspective.
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is the daily focus of participants. Skitch and An author in C˘at˘alin provides a mathemati-
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Hodgins defined problem gambling as a less judg- cian’s advice for safe and rational gambling, one
mental way of describing a repetitive pattern of of which is ”understanding your game.”
gambling that leads to serious destructive con- Recently, mathematical models involving non-
sequences and is beyond voluntary control. In integer order derivatives have gained significant
recent decades, problem gambling has become a attention because they are more accurate and re-
major public health issue. Problem gambling is alistic than classical models. 18–20 An important
a repetitive behavior, despite harm and negative question that led to the birth of fractional-order
consequences. It is an addictive behavior with calculus in 1695 came from the letter L’Hopital
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high comorbidity with alcohol problems. In the sent to Leibniz. The Riemann and Liouville def-
past two decades, the world community has grad- inition fails to explain the importance of start-
ually come to accept that addiction is a type of ing conditions. The Caputo derivative addresses
disease. Recently, gambling problems have been this problem, but when defined with a power-
recognized as a major public health issue in mod- law kernel, it has a notable limitation owing
ern society. The clinical definition of problem to its singular nature. 21 The exponential decay
gambling was determined using the Diagnostic kernel definition by Caputo and Fabrizio ad-
and Statistical Manual, 4th Edition, Test Revi- dressed the issue of singularity but introduced
sion (DSM-IV-TR) symptom checklist (American a locality problem. The first definition of a
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Psychiatric Association [APA]). According to a non-singular arbitrary order derivative by Caputo
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study in Room et al., problem gambling leads and Fabrizio significantly contributed to the con-
to several social and psychological problems, in- cept of non-singular kernel fractional calculus. A
cluding depression and alcohol and drug depen- novel fractional-order Caputo–Fabrizio operator,
dence. Research findings related to problem gam- derived in 2015, 22 addresses several linear and
bling suggest that this disorder is a real issue that nonlinear issues. The fractional operator is fre-
needs to be addressed as a public health concern. quently used in various branches of mathematics
and engineering. Many authors have applied this
fractional operator to investigate the behavior of
Over the last two decades, excessive gambling
mathematical models (see 23 and references cited
has been a primary subject of analysis and in-
therein). Non-local and non-singular operators
vestigation in mathematics and statistics. Sev-
are key reasons why fractional calculus is becom-
eral mathematical models have been formulated
ing increasingly popular. A few years ago, signif-
to understand the dynamics of excessive gam-
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bling better. For example, Do and Lee used icant efforts were made to find more interesting
a simple compartmental model to explore gam- and novel non-singular arbitrary order derivatives
bling dynamics by focusing on young people’s based on kernels. Atangana and Baleanu studied
gambling. In that study, the basic reproduction a well-known non-singular derivative within the
number was R 0 = 1.466. The authors of Kong Mittag-Leffler kernel in 2016 and used it to solve
24
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et al. analyzed online gambling on scale-free net- various science and engineering problems. This
25
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works. Shaffer and Korn viewed problems associ- operator was recently updated.
ated with gambling as a socially transmitted dis- In recent years, many global issues have been
ease. In Young and Tae, 10 Lee and Do examined modeled using arbitrary order calculus. 26 Moti-
the dynamics of gambling among older adults. vated by the advancement of arbitrary order cal-
The authors of ref. 11 investigated impulsivity tra- culus, many authors have focused on studying
jectories and gambling in adolescence. The au- the results of nonlinear differential equations with
thors of ref. 12 focused on the reduction of atten- a fractional operator by developing various ana-
tional blink for gambling-related stimuli in prob- lytical, semi-analytical, and fully numerical tech-
lem gamblers. Brown et al. 13 investigated the dif- niques to find approximate solutions.
ferences between problem and non-problem gam- The primary reason for using non-integer
blers in electronic machine games. Coping strate- order derivative models is that many sys-
gies in adolescents with gambling problems were tems exhibit memory, history, or non-local ef-
the main study objective of the paper in Gupta fects, which are challenging to model with
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