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Some new Gompertz fractional difference equations

Tom Cuchta and Brooke Fincham

Vol. 13 (2020), No. 4, 705–719
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.

Keywords
discrete fractional calculus, Gompertz, parameter estimation, data fitting
Mathematical Subject Classification
Primary: 39A60
Secondary: 26A33, 92D25, 33E12
Milestones
Received: 29 April 2020
Revised: 6 August 2020
Accepted: 10 August 2020
Published: 20 November 2020

Communicated by Martin J. Bohner
Authors
Tom Cuchta
Department of Computer Science and Mathematics
Fairmont State University
Fairmont, WV
United States
Brooke Fincham
Department of Computer Science and Mathematics
Fairmont State University
Fairmont, WV
United States