A curative and preventive treatment fractional model for plant disease in Atangana–Baleanu derivative through Lagrange interpolation

Abstract

The growth of the world populations number leads to increasing food needs. However, plant diseases can decrease the production and quality of agricultural harvests. Mathematical models are widely used to model and interpret plant diseases, showing viruses’ transmission dynamics and effects. In this paper, we investigate the dynamics of the treatments of plant diseases via the Atangana–Baleanu derivative in the sense of Caputo (ABC). We study the existence and uniqueness of solutions of curative and preventive treatment fractional model for plant disease. By using Lagrange interpolation, we give numerical simulations and investigate the results at various fractional orders under specific parameters. The results show that the increase of the roguing rate for the most infected plant or the decrease of the rate of planting in the infected area will reduce the plant disease transmissions. For balancing the plant production, the decision-makers can plant in other areas in which there are no infected cases.

A Mini-Review on Recent Fractional Models for Agri-Food Problems

“…The authors used two fractional operators, namely, the Caputo and the Caputo-Fabrizio fractional derivatives. In [30], the authors studied the dynamics of the treatments of plant diseases Acknowledgments: The authors would like to thank the anonymous reviewers and the associate editor in charge of handling this paper for their comments and criticisms. Their suggestions were literally followed, and they helped in improving the quality of this mini-review.…”

Stability and existence of solutions to a class of Atangana-Baleanu-Caputo coupled fractional differential equations

“…The Atangana-Baleanu(AB) fractional order derivatives defined by Atangana and Baleanu are widely used in many fields such as biology, control science and engineering, and dynamical system, etc. For example, Owolabi and Atangana [15] used AB fractional order derivatives to build Adams-Bashforth format to model chaotic problems; Abdullahi and Yusuf [16] discussed the AB fractional order derivatives in the Caputo sense to analyze popular mathematical models involving two vaccines, not only simplifying the original ordinary differential equation model and matching the findings to the classical case, but also the fractional order model retains all memory effects, making the model a better match to the AB fractional order derivatives in the Caputo sense; Gupta and Kumar [17] developed an image denoising model using Caputo, Caputo-Fabrizio and AB fractionalorder integration to verify the effectiveness of the method compared to the traditional fractional-order model using multiple parameter simulation results; Abdullah and Huang [18] analyzed the application of AB derivatives in the Caputo sense to a fractional model for plant disease control. More applications can refer [19][20][21][22][23][24][25].…”