In the cultivation of Capsicum annuum (C. annuum), the major obstacles are triggered by the Yellow virus (Gemini virus). The virus is spread through insects, namely Bemisia tabaci (B. tabaci). To reduce the spreading of the virus in C. annuum, the entomopathogenic fungi (Verticillium lecanii) are used. We have analyzed the fractional-order model of chili plants with Atangana–Baleanu derivative (AB-derivative). Also, we calculate the numerical values to illustrate the results.