A Fractional-Order Mathematical Model of Banana Xanthomonas Wilt Disease Using Caputo Derivatives (Contemporary Mathematics, 2024)
This article investigates a fractional-order mathematical model of Banana Xanthomonas Wilt disease while considering control measures using Caputo derivatives. The proposed model is numerically solved using the L1-based predictor-corrector method to explore the model’s dynamics in a particular time range. Stability and error analyses are performed to justify the efficiency of the scheme. The non-local nature of the Caputo fractional derivative, which includes memory effects in the system, is the main motivation for incorporating this derivative in the model. We obtain varieties in the model dynamics while checking various fractional order values.
Keywords: mathematical model; Caputo fractional derivative; L1 predictor-corrector scheme; error analysis; stability; graphical simulations