A combination of time-scale calculus and a cross-validation technique used in fitting and evaluating fractional models |
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Authors: | Amera AlmusharffNgoc Nguyen |
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Affiliation: | Department of Mathematics, Western Kentucky University, Bowling Green, KY 42101, USA |
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Abstract: | In this work, we demonstrate how fractional calculus and time-scale calculus can be combined beautifully to solve and fit a modeling problem. In addition, a cross-validation technique is used to evaluate the fitted model. The specific application that we consider is the one-compartment model. The one-compartment model is a first-order differential equation that describes drug concentration over time. It turns out that approximating the solution by using a fractional model allows us to get more accurate results for model fitting. To quantitatively verify this insight, we compare between a first-order model and anα-order fractional model using real data for drug concentration. Then the mean squared error and a cross-validation method are used to determine the model that provides the best fit and predictions for unseen data. |
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Keywords: | Fractional calculus Time-scale calculus One-compartment model Best fitting model Cross-validation Best prediction model |
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