Mathematical modeling of the dynamics of plastic production and recycling under environmental constraints

Plastics are a necessary component of daily living. There are serious concerns about the environmental effects of non-biodegradable plastics in landfills. Plastic production generates significant plastic waste daily. Plastic waste is a representative waste product originating from industrial development, and its discharge into the environment causes severe environmental problems. Hence, plastic recycling has been a vital measure to reduce plastic waste. In this study, we have proposed a novel mathematical model that considers significant elements such as plastic production, plastic waste, and recycling of waste. This study uses two fractional derivatives, the Caputo and Caputo-Fabrizio derivatives, and thoroughly compares them to determine how well the derivatives work with the dynamical model. The fractional order model’s existence, uniqueness, boundedness, and local and global stability are examined. We have used the Fractional Linear Multistep Method (FLMM) to solve both models. Numerical simulations show how our models predict the values of the variables and fit the actual data. Furthermore, we have compared numerical methods (Fractional RK4 and FLMM) to comprehend the models’ behavior. A parameter analysis was conducted for each parameter to examine the behavior when the values are varied. This work offers a mathematical viewpoint on the real-world difficulties of managing plastic waste and recycling. By examining the variables in the model, we can provide insights into how these parameters change over time. Fractional derivative comparison aids in identifying the best method for simulating such intricate systems. Environmental planners and policymakers can use these insights to help create sustainable waste management plans and more effective recycling programs.