López Pouso Rodrigo and Márquez Albés Ignacio: Resolution methods for mathematical models based on differential equations with Stieltjes derivatives. (2019)
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Abstract
Stieltjes differential equations, i.e. differential equations with usual derivatives replaced by derivatives with respect to given functions (derivators), are useful to model processes which exhibit dead times and/or sudden changes. These advantages of Stieltjes equations are exploited in this paper in the analysis of two real life models: first, the frictionless motion of a vehicle equipped with an electric engine and, second, the evolution of populations of cyanobacteria Spirullina plantensis in semicontinuous cultivation processes. Furthermore, this is not only a paper on applications of known results. For the adequate analysis of our mathematical models we first deduce the solution formula for Stieltjes equations with separate variables. Finally, we show that differential equations with Stieltjes derivatives reduce to ODEs when the derivator is continuous, thus obtaining another resolution method for more general cases.
| Item Type: | Journal |
|---|---|
| Publication full: | Electronic journal of qualitative theory of differential equations |
| Date: | 2019 |
| Number: | 72 |
| ISSN: | 1417-3875 |
| Page Range: | pp. 1-15 |
| DOI: | 10.14232/ejqtde.2019.1.72 |
| Uncontrolled Keywords: | Differenciaegyenlet, Matematikai modell |
| Additional Information: | Bibliogr.: 15. p. ; összefoglalás angol nyelven |
| Date Deposited: | 2020. Jan. 27. 11:07 |
| Last Modified: | 2021. Sep. 16. 10:42 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/64716 |
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