A fractional dynamical model for honeybee colony population

Bees are the main contributors of pollination and it is predicted that disruption of pollination causes some serious problems in economics, agriculture and ecology. It has been reported that honeybee colony collapse has increased dramatically for some time in different parts of the world. In order to investigate the causes of colony collapse, we establish a fractional multi-order honeybee colony population model. Two different models with Caputo and Caputo-Fabrizio differentiation operators have been compared. We justify the existence and uniqueness of the solution. Stability analysis has been presented. We find the numerical values of the fractional order (p,q) so that the numerical results are close to the experimental findings more than the integer-order case.