Exact and discretized stability of the Bagley–Torvik equation

• Fractional model of the motion of a thin plate in a Newtonian fluid is analysed.
• Qualitative properties of the true and numerical solutions are described.
• Numerical stability regions for the classical and fractional models are compared.

The paper discusses stability and asymptotic properties of a two-term linear fractional differential equation involving the Bagley–Torvik equation as the particular case. These properties are analysed for the exact as well as numerical solutions obtained from the Grünwald–Letnikov discretization of the studied differential equation. As the main results, precise descriptions of the exact and discretized stability regions are presented, including the decay rate of the solutions. These results enable us, among others, to observe similarities and distinctions between the asymptotic behaviour of the classical and fractional damping models.