Cao Labora, DanielTenreiro Machado, José António2020-04-292020-04-292020Cao Labora, D.; Tenreiro Machado, J.A. Existence of Bounded Solutions to a Modified Version of the Bagley–Torvik Equation. Mathematics 2020, 8, 289.http://hdl.handle.net/10347/21885This 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.eng© 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/)http://creativecommons.org/licenses/by/4.0/Fractional CalculusBagley–Torvik EquationLimit BehaviorBounded Solutionsjournal article10.3390/math80202892227-7390open access