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Image of Vibration Testing and System Dynamics
ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

A Novel Fractional-Order Model for Alcohol Consumption Dynamics: Evaluating Social and Economic Interventions

Journal of Vibration Testing and System Dynamics 10(2) (2026) 135--146 | DOI:10.5890/JVTSD.2026.06.003

R. Jayakumar$^{1}$, V. Kavitha$^{2}$, M. Mallika Arjunan$^{3}$, R. Deepa$^{4}$, T.R. Ramesh Rao$^{5}$

$^{1}$ Research Scholar, Department of Mathematics & Actuarial Science, B.S. Abdur Rahman Crescent Institute of Science & Technology, Chennai-600048, Tamil Nadu, India; Department of Mathematics, Kings Engineering College, Sriperumbudur-602117, Tamil Nadu, India

$^{2}$ Department of Mathematics, School of Sciences, Arts, Media & Management, Karunya Institute of Technology and Sciences, Karunya Nagar, Coimbatore-641114, Tamil Nadu, India

$^{3}$ Department of Mathematics, School of Arts, Sciences, Humanities and Education, SASTRA Deemed to be University, Thanjavur-613401, Tamil Nadu, India

$^{4}$ Department of Mathematics, Panimalar Engineering College, Chennai–600123, Tamil Nadu, India

$^{5}$ Department of Mathematics & Actuarial Science, B.S. Abdur Rahman Crescent Institute of Science & Technology, Chennai-600048, Tamil Nadu, India

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Abstract

In this paper, we propose a new fractional-order mathematical model of alcohol drinking behavior involving the conformable fractional derivative $\c$ and eight interconnected compartments, incorporating the socio-economic distinction between private and public addiction treatment centers. The model explicitly accounts for road accidents and alcohol-induced violence as separate classes, emphasizing the societal impact of heavy drinking. We establish the existence and uniqueness of solutions and analyze the Ulam-Hyers (U-H) stability of the model using fixed-point theory, ensuring the robustness of the theoretical framework. Numerical simulations further validate the theoretical results under varying fractional orders of $\c$, demonstrating that higher memory effects in fractional dynamics lead to slower addiction recovery and prolonged intervention impact. Additionally, model validation using real-time data reinforces its applicability to real-world scenarios, demonstrating the model’s potential for guiding policy decisions and treatment strategies.

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