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.
Keywords
discrete fractional calculus, Gompertz, parameter
estimation, data fitting
