Design of a Fractional-Order Intelligent Traffic Control System Using Caputo Modelling and FNSS-Based Neural Learning

The increasing complexity of urban traffic, driven by rapid urbanization and unpredictable vehicular behavior, poses a significant challenge to traditional traffic control systems. (Zheng et al., 2014; Kwon et al., 2004) These conventional systems often lack adaptability, memory-awareness, and the ability to handle uncertainty in real time. (Englund et al., 2021) To address these limitations, this study proposes a novel hybrid intelligent traffic control framework that integrates Caputo fractional-order modeling, Fermatean Neutrosophic Soft Sets (FNSS), and Artificial Neural Networks (ANNs). The Caputo system models traffic dynamics with memory, enabling accurate forecasting of congestion patterns by considering historical data. (Podlubny, 1998; Diethelm, 2010; Li & Zeng, 2015; Machado et al., 2018) FNSS logic handles real-time uncertainty, vagueness, and sensor ambiguity, while the neural network layer learns and optimizes signal control decisions through historical and real-time data. (Ye, 2020; Broumi & Smarandache, 2021; Çelik et al., 2022) Simulation and implementation were conducted using the SUMO traffic simulator and Python-based TraCI API, enhanced by reinforcement learning modules for adaptive control. (Krajzewicz et al., 2012; Behrisch et al., 2011; Mannion et al., 2016; Wei et al., 2019; van der Pol & Oliehoek, 2016) The results showed that traffic got a bit better — there was around 6.27% less congestion, waiting times improved by 4.81%, and cars passed through intersections about 7.2% faster. Also, there was a clear drop in CO₂ emissions and the time people had to wait to cross the street. (Sun et al., 2017; Barth & Boriboonsomsin, 2009) This study proves that mixing memory-based models with smart AI that can deal with uncertain data works well. (Machado et al., 2018; Englund et al., 2021) But it's not just about numbers — the system we built could help connect with smart city tools, live traffic screens, and even future self-driving car systems. (Zheng et al., 2014; Englund et al., 2021; Zhang et al., 2018) All of this together can lead to safer roads, less pollution, and smoother traffic in busy cities. (Sun et al., 2017; Barth & Boriboonsomsin, 2009)