Application Of Fractional Calculus in Modeling and Reducing Road Accidents

Abstract

Abstract Traditional mathematical models of traffic flow and driver behavior rely on integer-order calculus, which assumes localized, instantaneous changes. However, real-world traffic systems exhibit strong memory effects, non-local interactions, and anomalous diffusion. This paper explores the application of fractional calculus utilizing non-integer orders in reducing road accidents. By integrating fractional derivatives into traffic flow dynamics, viscoelastic tire-road friction models, and advanced driver assistance systems (ADAS), we demonstrate how capturing hereditary properties can optimize highway design, vehicular control, and active safety systems to actively prevent collisions.