The presence of sulfamethazine (SMZ) in the environment poses significant risks to both ecological systems and human health, necessitating the development of efficient degradation methods. This study presents a novel approach for synthesizing green carbon dots (G-CDs) using expired folic acid tablets as a single precursor through a one-pot hydrothermal process for the photodegradation of SMZ, which has not been reported before. Notably, green-synthesized carbon dots (G-CDs) exhibited superior performance compared to those synthesized from pure folic acid (FA-CDs) toward SMZ photodegradation. The results demonstrated that under simulated sunlight irradiation, G-CDs achieved over 94% degradation of SMZ within 75 min, while FA-CDs only degraded around 10% of SMZ. Full SMZ photodegradation was realized under optimal conditions. Further investigation into the kinetics and photogenerated charge carriers revealed that the photocatalytic degradation mechanism of SMZ was mainly due to holes, hydroxyl radical and superoxide anions. These findings emphasize the potential of green-synthesized G-CDs as highly efficient photocatalysts for environmental remediation applications, particularly in the degradation of organic pollutants.

In the last few decades, fractional calculus has been used in many applications such as chaotic models [1], biological population models [2], fluid mechanics [3], neural networks [4], and signal processing [5]. Compared to integer-order derivatives, fractional-order (FO) ones offer a great tool for describing memory and the inherited characteristics of distinct materials and processes [6]. Therefore, using FO derivatives instead of integer-order ones may yield more accurate results. The FO hyperchaotic complex systems have been studied [7, 8]. On the other hand, Caputo put forward the concept