On a viscoelastic rod with constitutive equation containing fractional derivatives of two different orders

摘要

We study lateral vibration of a viscoelastic rod with a generalized fractional derivative constitutive equation. We show that the motion of the rod is governed by a system of linear partial differential equations with fractional derivatives. The existence, analytical form and properties of solutions to these equations is studied. The conditions of stability, i.e. boundness of the solution, is studied in detail.