Applied modeling of smoking behavior: a computational approach using generalized caputo formulation

Smoking remains one of the leading causes of preventable health issues worldwide, and efforts to reduce its prevalence are more crucial than ever. This study explores the effectiveness of nicotine gum and media campaigns in shaping smoking behavior. It introduces a fractional dynamic model grounded in both generalized and Caputo formulations, utilizing Euler’s approach to capture the interactions within this complex system. When the parameter equals 1, the generalized Caputo model simplifies to the classic Caputo model. To ensure the model’s reliability, its existence and uniqueness are validated using the Schauder and Banach fixed point theorems, while stability is assessed with the Ulam-Hyers criterion. The model provides valuable insights into the spread of smoking habits, offering strategies to reduce the number of active smokers, highlight the risks of smoking, and encourage permanent quitters. Additionally, the study includes graphical representations that illustrate the model’s predicted behaviors and a thorough analysis of the fractional approach.