Some new Gompertz fractional difference equations

Abstract

We introduce three new fractional Gompertz difference equations using the Riemann–Liouville discrete fractional calculus. These three models are based a nonfractional Gompertz difference equation, and they differ depending on whether a fractional operator replaces the difference operator, the integral operator defining the logarithm, or both simultaneously. An explicit solution to one of them is achieved with restricted parameters and recurrence relation solutions are derived for all three. Finally, we fit these models to data to compare them with a previously published discrete fractional Gompertz model and the continuous model.