Existence of Bounded Solutions to a Modified Version of the Bagley–Torvik Equation

Daniel Cao Cao Labora, José António Tenreiro Tenreiro Machado
2020 Mathematics  
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
more » ... ich has a clear physical meaning.
doi:10.3390/math8020289 fatcat:76x5t4dg5vdyxghxvl7zxnbasa