A fractional mathematical modeling of protectant and curative fungicide application

Fungicides are consumed to foreclose or slow the epidemics of disease germ by fungi. Crop cultivation is a favorable business platform for farmers, but it is also very common for them to have losses. These losses happen by attacking pathogens, such as fungi, oomycetes (water fungi), viruses, bacteria, nematodes, and viroid that spread the infection into the plants. In this article, we derive a fractional mathematical model for simulating the dynamics of fungicide application via Caputo-Fabrizio fractional derivative. Caputo-Fabrizio operator is defined with non-singular type kernel which is better than singular kernel. We give some important proofs related to the existence of a unique solution of the given model. We derive the solution of the model by using the Adams-Bashforth algorithm and also mentioned the stability of the method. We plotted the number of graphs at different fungicide application rate, fungicide decay rate, fungicide effectiveness, curatives rate of fungicide, growth rate of the host, and removal rate. A complete structure of the given problem can be understood by this paper. The main novelty of this work is to understand the role of fungicide application in the disease caused by fungi with the help of fractional derivatives consisting memory effects.