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Some new
Gompertz fractional difference equations
Tom Cuchta and Brooke Fincham |
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Vol. 13 (2020), No. 4, 705–719
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Abstract |
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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. |
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Keywords
discrete fractional calculus, Gompertz, parameter
estimation, data fitting
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Mathematical Subject Classification
Primary: 39A60
Secondary: 26A33, 92D25, 33E12
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Milestones
Received: 29 April 2020
Revised: 6 August 2020
Accepted: 10 August 2020
Published: 20 November 2020
Communicated by Martin J. Bohner
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Authors |
| Tom Cuchta | |
| Department of Computer Science and
Mathematics Fairmont State University Fairmont, WV United States |
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| Brooke Fincham | |
| Department of Computer Science and
Mathematics Fairmont State University Fairmont, WV United States |
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| © 2020 MSP (Mathematical Sciences Publishers). |
