Mathematical Model of the Waste Plastic Management via ABC Fractional Order Derivative

Plastic waste can be broadly classified as recyclable and nonrecyclable wastes. The United Nations has set 17 goals of which Goal 14 refers to “Life below Water.†If plastic waste is not properly managed, it can pose a health hazard, including reproductive impairment in marine species. Hence, waste plastic management is necessary to achieve the Goal No. 14 of the SDG Goals of the United Nations, 2030. The primary objective of this paper is to analyze a fractional model of plastic waste management using the recently introduced ABC-type fractional derivative and to closely examine the plastic waste management model. The Picard ‘Lindelof’ approach is used to investigate their existence and uniqueness. In addition, we obtain approximate solutions of the ABC fractional order waste plastic management model using a numerical technique that combines the ABC fractional derivative with the fundamental theorem of fractional calculus and Lagrange polynomial interpolation. Numerical simulations are used to demonstrate the impact of control parameters on specific compartments within the model and its novelty over other models, supplemented by graphical representations. In this work, we have validated our proposed model by substituting the plastic surface index (PSI) for the fractional order h, which lies in 0,1. A comparison is also made between plastics or polyethylene and polyvinyl chloride, and the effect of PSI has also been analyzed, so that necessary corrective steps can be taken by the competent authority to achieve SDG Goal 14 and other related goals such as 11, 12, 15, and 17.