Fractional Calculus to Analyze Efficiency Behavior in a Balancing Loop in a System Dynamics Environment

Abstract

This research project focuses on developing a mathematical model that allows us to understand the behavior of the balancing loops in system dynamics in greater detail and precision. Currently, simulations give us an understanding of the behavior of these loops, but under the premise of an ideal scenario. In practice, however, accurate models often operate with varying efficiencies due to various irregularities and particularities. This discrepancy is the primary motivation behind our research proposal, which seeks to provide a more realistic understanding of the behavior of the loops, including their different levels of efficiency. To achieve this goal, we propose the introduction of fractional calculus in system dynamics models, focusing specifically on the balancing loops. This innovative approach offers a new perspective on the state of the art, offering new possibilities for understanding and optimizing complex systems.