Agricultural and Biological Research

A fractional differential approach to plant pest mature and immature biological enemy

Anil Kumar Shukla*, Joydip Dhar, Rajshree Mishra

The issue of plant pests is a critical area of investigation at present. While numerous chemical solutions are available, their toxic effects make the use of natural enemies a preferable alternative. This article introduces a fractional calculus approach to model the dynamics between mature and immature natural enemies of plant pests. The study discusses the existence and uniqueness of the solution, the non-negativity of the solution and both global and local stability of the equilibrium point. Given that memory is intrinsic to biological systems, the proposed technique is advantageous due to the memory effect of fractional derivatives, leading to more accurate solutions. Simulations with different fractional parameters generate optimal solutions.