Mathematical modeling study demonstrates how fractional derivatives enhance collision prevention frameworks, suggesting novel approaches to vehicular control.
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.
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S. V. Nakade (2026) studied this question.
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