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.
Highlights
It is presently recognized that fractional calculus (FC) has a vast horizon of possible applications [1,2,3,4,5,6,7,8]
Several applications to the dynamics of particles can be found in [16]. This interconnection between FC and real models is natural in the framework of fluid dynamics [17]
The aim of this manuscript is to study in detail some aspects regarding the Bagley–Torvik equation (BTE)
Summary
It is presently recognized that fractional calculus (FC) has a vast horizon of possible applications [1,2,3,4,5,6,7,8]. This interconnection between FC and real models is natural in the framework of fluid dynamics [17] The aim of this manuscript is to study in detail some aspects regarding the Bagley–Torvik equation (BTE). This fractional differential equation (FDE) models the vertical motion of a thin large plate immersed in a Newtonian fluid and hung by a spring, under the action of an external force (or source term). This result is obtained after describing the solution to our problem as a result of applying a fractional integral operator to the solution of an ordinary differential equation (ODE).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
