Existence of Bounded Solutions to a Modified Version of the Bagley–Torvik Equation
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Título: | Existence of Bounded Solutions to a Modified Version of the Bagley–Torvik Equation |
Autor/a: | Cao Labora, Daniel Tenreiro Machado, José António |
Centro/Departamento: | Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización |
Palabras chave: | Fractional Calculus | Bagley–Torvik Equation | Limit Behavior | Bounded Solutions | |
Data: | 2020 |
Editor: | MDPI |
Cita bibliográfica: | Cao Labora, D.; Tenreiro Machado, J.A. Existence of Bounded Solutions to a Modified Version of the Bagley–Torvik Equation. Mathematics 2020, 8, 289. |
Resumo: | This manuscript reanalyses the Bagley–Torvik equation (BTE). The Riemann–Liouville fractional differential equation (FDE), formulated by R. L. Bagley and P. J. Torvik in 1984, models the vertical motion of a thin plate immersed in a Newtonian fluid, which is held by a spring. From this model, we can derive an FDE for the particular case of lacking the spring. Here, we find conditions for the source term ensuring that the solutions to the equation of the motion are bounded, which has a clear physical meaning. |
Versión do editor: | https://doi.org/10.3390/math8020289 |
URI: | http://hdl.handle.net/10347/21885 |
DOI: | 10.3390/math8020289 |
E-ISSN: | 2227-7390 |
Dereitos: | © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) |
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