AN EFFECTIVE NUMERICAL METHOD FOR STUDYING THE FRACTAL-FRACTIONAL SMOKING MODEL

M. Adel, M. M. Khader, I. Alraddadi, N. H. Sweilam, M. B. Riaz and Hijaz Ahmad
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M. Adel: Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, KSA
M. M. Khader: ��Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia‡Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
I. Alraddadi: Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, KSA
N. H. Sweilam: �Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
M. B. Riaz: �IT4Innovations, VSB-Technical University of Ostrava, Ostrava, Czech Republic∥Department of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon
Hijaz Ahmad: Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, KSA**Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia 99138, Turkey††Department of Mathematics, College of Science, Korea University, Seoul 02841, Republic of Korea‡‡Department of Technical Sciences, Western Caspian University, Baku 1001, Azerbaijan

FRACTALS (fractals), 2025, vol. 33, issue 03, 1-13

Abstract: Worldwide, smoking is a common social practice, especially in places like schools and on important occasions. The World Health Organization (WHO) states that smoking is the third leading cause of death worldwide and the most significant avoidable cause of disease. Thus in this study, we present the solution behavior of the fractal-fractional (FF) smoking model. Using an effective numerical integration technique, the discretized system of FF differential equations that results is numerically integrated. By using RK4 to evaluate the numerical solution, we can meet the requirements for both efficiency and accuracy in the given approach. In the hope of providing some recommendations through which to reduce the risks of this bad behavior, the effect of some parameters and external factors affecting the solution behavior of this proposed mathematical model was studied, including the recruitment rate (due to immigration or birth) and the smoking cessation rate. The results show that the implemented technique is a straightforward and efficient tool for modeling the solution for these models.

Keywords: RK4; Numerical Integration; Smoking Model; Caputo Fractal-Fractional Derivative (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X24400504

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