The rising tide of smoking-related diseases has irreparably damaged the health of both young and old people, according to the World Health Organization. This study explores the dynamics of the age-structure smoking model under fractal-fractional (F-F) derivatives with government intervention coverage. We present a new fractal-fractional model for two-age structure smokers in the Caputo–Fabrizio framework to emphasize the potential of this operator. For the existence-uniqueness criterion of the given model, successive iterative sequences are defined with limit points that are the solutions of our proposed age-structure smoking model. We also use the functional technique to demonstrate the proposed model stability under the Ulam–Hyers condition. The two age-structure smoking models are numerically characterized using the Newton polynomial. We observe that in Groups 1 and 2, a change in the fractal-fractional orders has a direct effect on the dynamics of the smoking epidemic. Moreover, testing the inherent effectiveness of government interventions shows a considerable impact on potential, occasional, and temporary smokers when the fractal-fractional order is 0.95. It is the view that this study will contribute to the applicability of the schemes, the rich dynamics of the fractal, and the fractional perspective of future predictions.

In data mining, and statistics, anomaly detection is the process of finding data patterns (outcomes, values, or observations) that deviate from the rest of the other observations or outcomes. Anomaly detection is heavily used in solving real-world problems in many application domains, like medicine, finance , cybersecurity, banking, networking, transportation, and military surveillance for enemy activities, but not limited to only these fields. In this paper, we present an empirical study on unsupervised anomaly detection techniques such as Density-Based Spatial Clustering of Applications with Noise (DBSCAN), (DBSCAN++) (with uniform initialization, k-center initialization, uniform with approximate neighbor initialization, and $k$-center with approximate neighbor initialization), and $k$-means$--$ algorithms on six benchmark imbalanced data sets. Findings from our in-depth empirical study show that k-means-- is more robust than DBSCAN, and DBSCAN++, in terms of the different evaluation measures (F1-score, False alarm rate, Adjusted rand index, and Jaccard coefficient), and running time. We also observe that DBSCAN performs very well on data sets with fewer number of data points. Moreover, the results indicate that the choice of clustering algorithm can significantly impact the performance of anomaly detection and that the performance of different algorithms varies depending on the characteristics of the data. Overall, this study provides insights into the strengths and limitations of different clustering algorithms for anomaly detection and can help guide the selection of appropriate algorithms for specific applications.