Exploring the relationship dynamics between farmers and mediators through the lens of the Caputo fractional derivatives

Abstract

This study aims to propose a mathematical model in the frame of fractional derivative, that explores the relationship between crops, farmers, and intermediaries. To model this dynamics of the interaction between crops, farmers, and intermediaries, we employ the three-species Lotka–Volterra Holling type-I model. Existence and uniqueness of the solution are examined by defining Picard’s operator and Banach fixed point theorem. We have derived sufficient conditions for the local and global stability of the equilibrium points. Additionally, we conduct numerical simulations to demonstrate the effects of key parameters on the dynamics of the state variables of the system using the generalized Adams–Bashforth–Moulton method. Collecting the data from authorized sources, we have validated the arguments made in the present study.

Keywords

• Lotka–Volterra model
• Predictor–corrector method
• Holling type-I functional response