Fractional order model for yield through diagnosed/undiagnosed soil

Abstract

Farming is the basic economy of any country. Soil fertility and water are key resources for yielding. The fractional order compartmental model is prepared in Caputo sense to improve the density of yield through diagnosed and undiagnosed soil. To measure the growing intensity of yield, the basic reproduction number is formulated using the next generation matrix method for integer order non-linear dynamical system. Local stability analysis is described for both the equilibrium points; undiagnosed soil free and optimum equilibrium point. Global stability is exhaustively computed by generating a Lyapunov function. With reference to the basic reproduction number, bifurcation analysis has been defined which expresses the chaotic nature of soil fertility. Moreover, optimal control theory is applied in the present fractional model to optimize yield. And optimality conditions are calculated with the help of Pontryagin maximum principle. The numerical simulation for different fractional orders is performed concerning validated data to analyze the behavior with respect to the order.

Fractional-order model on vaccination and severity of COVID-19

“…A predator–prey and rabies model using a fractional-order derivative was developed by Ahmed et al [ 13 ]. A fractional SIR model was created by Shah et al [ 8 , 9 ]. For the analysis of nonlinear fractional-order models, Shah et al [ 14 ] contrasted the Euler method (MEM) with nonstandard finite difference (NSFD).…”

“…In order to simulate the COVID-19 outbreak, Higazy [6] created a fractional SIDARTHE model with continuous function, state variables, and controls. To stop the spread of COVID-19, Shah et al [7] used optimal control, and Shah et al [8,9] used fractional optimal control. A dynamics and control on COVID-19 using fractional derivative for India was developed by Shaikh et al [10].…”