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

Abstract

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.

Keywords

• fractional calculus
• bagley–torvik equation
• limit behavior
• bounded solutions