Fractional Order Commensurate Model of Contaminated Soil–Plant Interaction with Non-singular Kernel

The inhabitation of crop cultivation is due to the absorption of heavy metals which can be forecasted by a known mathematical model. In this work, the non-singular Atangana Baleanu Caputo fractional order model of heavy metal transfer from soil to plant concentration is considered with three compartments: polluted soil, plant growth, and metabolic activities of soil–plant interactions. The existence of equilibrium points for various interactions of the pollution transformation is found. Stability analyses are carried out for different equilibrium points. A special type of Mittag-Leffler-Hyer-Ulam stability analysis is done using a fixed-point theorem. The numerical approximation solution to the Atangana Baleanu Caputo Soil–Plant interaction model is analyzed by using Adams Bashforth method. Numerical simulations are carried out using MATLAB. The essential and non-essential heavy metals accumulated by the paddy field are examined in the Kalpakkam, Tamil Nadu, and South India study areas. Finally, the study on the effect of the concentration of heavy metals at a low cost exhibits the magnificent behavior of the system.