Modeling and Evaluating Passengers′ Opinion Using Fractional‐Order Derivatives and Optimal Control Approaches

Abstract

Increasingly, rail passengers seek to experience higher quality services. Therefore, it is essential to identify and execute the most efficient improvement strategies that enhance passenger satisfaction. In order to achieve this goal, this research centers on formulating a compartmental model to examine passengers′ perceptions of rail services as a dynamic system and a corresponding optimal control problem. The researcher proves that the model has a unique, nonnegative, and bounded solution. Additionally, by applying Pontryagin′s maximum principle, the researcher derives optimal control strategies for the problem, enhancing operational efficiency and minimizing passenger dissatisfaction. The researcher also conducts numerical simulations using the ODE45 solver to analyze how the model solutions evolve over time. The numerical simulations demonstrate that the fractional derivative′s order significantly influences how passenger satisfaction changes over time. The findings reveal that the most effective strategies for enhancing passenger satisfaction include implementing measures such as improving the reliability and timeliness of train services as well as maintaining high safety and security standards. Rail operators are advised to prioritize these measures accordingly.