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An Exploration of Discrete Fractional Calculus with Applications to Intermittent Oncological Modeling |
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PP: 521-538 |
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doi:10.18576/pfda/110307
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Author(s) |
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Casey J. Mills,
Raegan Higgins,
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Abstract |
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| In this work, we use and unify time scale calculus and discrete fractional calculus to develop a new approach to modeling intermittent androgen deprivation therapy, a standard prostate cancer treatment. The novel time scale model previously developed assumes a constant length of time for on- and off-treatment intervals. By creating a time scale that more accurately represents time data, we explore the use of fractional calculus to model treatment. Current fractional calculus theory only allows for strictly continuous or discrete domains. We create a strictly discrete time scale and construct a dynamic equation on this time scale. We then develop theory that allows us to calculate the fractional difference of this dynamic equation. Finally, we model intermittent androgen deprivation therapy using this fractional difference and find that an improved fit is achieved for most of the patients tested.
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