Authors: Atanacković, Teodor
Pilipović, Stevan
Zorica, Dušan 
Title: An initial value problem arising in mechanics
Journal: Archive of Applied Mechanics
Volume: 84
Issue: 2
First page: 219
Last page: 233
Issue Date: 1-Feb-2014
Rank: M22
ISSN: 0939-1533
DOI: 10.1007/s00419-013-0795-9
We study an initial value problem for a system consisting of an integer order and a distributed-order fractional differential equation describing forced oscillations of a body attached to a free end of a light viscoelastic rod. An explicit form of a solution for a class of linear viscoelastic solids is given in terms of a convolution integral. Restrictions on storage and loss moduli following from the second law of thermodynamics play the crucial role in establishing the form of the solution. Some previous results are shown to be special cases of the present analysis.
Keywords: Distributed-order fractional differential equation | Forced oscillations of a body | Fractional viscoelastic material
Publisher: Springer Link

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