A fractional logistic approach for economic growth

A discrete logistic model is proposed for the Gross Domestic Product of an economy and its parameters are adjusted for some specific countries, taken from the Organization for Economic Co-operation and Development databases. Although this model fits “adequately” for some countries analyzed in this work, others show that it could be enhanced. A Caputo like fractional discrete model as a fractional version of the logistic one is presented, with the parameters stated previously. It is shown, by using the mean squared error, that this fractional version fits better for an economy whose behavior shows over time an isolated and unexpected boom period in its economy growth followed by a crisis period. For this type of dynamics, the fractional-order logistic equation improves the modeling given by an integer order logistic equation.