A fractional dynamics of a potato disease model

Abstract

Globally, potato is one of the staple foods eaten by a lot of people. It processed into different kinds of food for mankind. Climate change has brought a lot of changes with respect to the output of global food stock due to problems such as drought, diseases, etc. In this study, a potato disease model is formulated in a fractional-order derivative with the nonlocal and nonsingular operator (AB). The reproduction number of the potato model and the steady states are determined. The existence and uniqueness of solutions are established using the Banach space approach, and Hyers-Ulam stability is carried out to determine if the existence and uniqueness solution is stable. A numerical simulation is carried out with and without stochastic components, which indicates a similar result. However, the stochastic aspect depicts a random effect. It is established that the fractional-order derivative has effect on the dynamics of the potato disease.