Optimal control on ABC fractal fractional order model of micro-plastic pollution in soil and its effect on the nutrient cycle

Abstract

Micro-plastic pollution is the major ultimatum to contaminate agricultural soils and empirical situation to lessening the soil quality and fertility. In this work the soil pollution due to micro-plastic in the Atangana-Baleanu-Caputo fractal dimension and fractional order inquiry with four compartments namely, Microplastic (P(t)), Soil pollution (S(t)), Remediate or recycling (R(t)) and Soil Nutrients cycle (N(t)). The qualitative analysis of the steady states is explained as locally stable, globally stable and Hyer Ulam stable. The expected equilibrium point appears in a pollution-free equilibrium point and pollution-extinct equilibrium point. Two significant best control strategies (u1(t) and u2(t)) are found to reduce soil pollution. Sensitivity analyses bring off the nature of various deportment of Basic reproduction numbers. Numerical approximation extracted with the help of Newton's Polynomial method. The purpose of precise expected results is demonstrated as a numerical simulation for various orders (0≤α≤0.6) and dimensions.