A novel mechanism to simulate fractional order maize foliar disease dynamical model

Abstract

This paper presents a mathematical model to examine the effects of foliar diseases on the dynamics of maize plants. Our paper investigates a newly developed system of differential equations for maize foliar disease (MFD) in terms of fractional Atangana–Baleanu (AB), Caputo–Fabrizio (CF) and Caputo operators. The asymptotic stability at the equilibrium point of the non-integer system is calculated based on the reproduction number R. Our study utilized the fixed point postulate to investigate the uniqueness and existence of solutions. Furthermore, by examining the variance of each parameter, we have conducted a sensitivity analysis of the model. The generalized non-linear system with Atangana–Baleanu (AB), Caputo–Fabrizio (CF) and Caputo non-integer operators have been solved numerically via the Toufik–Atangana (TA) and Adams–Bashforth technique, respectively. We have demonstrated the applicability and effectiveness of these methods by analyzing numerical simulations for the non-integer maize foliar disease (MFD) model.

Keywords

• Maize foliar disease (MFD) model
• Caputo operator
• Local and global stability
• Caputo–Fabrizio (CF) operator
• Atangana–Baleanu (AB)
• Existence and uniqueness