Parameters Identification and Numerical Simulation for a Fractional Model of Honeybee Population Dynamics

Abstract

In order to investigate the honeybee population dynamics, many differential equation models were proposed. Fractional derivatives incorporate the history of the honeybee population dynamics. We numerically study the inverse problem of parameter identification in models with Caputo and Caputo–Fabrizio differential operators. We use a gradient method of minimizing a quadratic cost functional. We analyze and compare results for the integer (classic) and fractional models. The present work also contains discussion on the efficiency of the numerical methods used. Computational tests with realistic data were performed and are discussed.