Two compartmental fractional derivative model with fractional derivatives of different order |
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Authors: | Jovan K. Popović Stevan Pilipović Teodor M. Atanacković |
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Affiliation: | 1. Faculty of Medicine, Department of Pharmacology, Toxicology and Clinical Pharmacology, University of Novi Sad, 21000 Novi Sad, Serbia;2. Faculty of Science and Mathematics, Department of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, Serbia;3. Faculty of Technical Sciences, Institute of Mechanics, University of Novi Sad, 21000 Novi Sad, Serbia |
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Abstract: | This study presents a new two compartmental model that contains fractional derivatives of different order. The model is so formulated that the mass balance is preserved. In this way we give an answer on a claim that such a model is not possible. The generalization that includes nonlinear terms and fractional order dynamics between compartments is also discussed. We derived a physically correct two compartmental system (i.e., the one preserving the mass balance) by the use of the Taylor expansion formula. Moreover, we derived in the Appendix such a system preserving the mass balance without the use of the Taylor formula but by the use of mass balance for systems with equal order fractional derivatives. |
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