Chaotic dynamics in some fractional predator-prey models via a new Caputo operator based on the generalised Gamma function

We introduce a generalisation of the Caputo fractional differential operator by replacing the Euler Gamma function in the basic operator with the generalised Gamma function. The generalised Caputo operator has a new degree of freedom (fractional parameter) that affects the dynamics of the model. The basic mathematical properties of the generalised Caputo operator are discussed. Then, we apply this generalised fractional operator to some predator-prey models, such as the fractional Hastings-Powell food chain model and the fractional generalised Lotka-Volterra model. The simulation results show that the two systems exhibit a variety of chaotic attractors when the new operator's parameter is varied.

Automated summary

We propose a generalisation of the Caputo fractional differential operator using the generalised Gamma function instead of the Euler Gamma function. The new operator introduces a fractional parameter that influences the dynamics of the model. We explore the mathematical properties of the generalised Caputo operator and apply it to predator-prey models like the fractional Hastings-Powell food chain model and the fractional generalised Lotka-Volterra model. Simulation results demonstrate a variety of chaotic attractors in these systems when varying the parameter of the new operator.