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Mathematical Problems in Engineering
Volume 2015, Article ID 591715, 4 pages
Research Article

Analytical Solution of General Bagley-Torvik Equation

Escola Politécnica da Universidade de São Paulo, Avenida Prof. Luciano Gualberto, Travessa 3, No. 158, 05508-900 São Paulo, SP, Brazil

Received 21 October 2015; Accepted 18 November 2015

Academic Editor: Ivan D. Rukhlenko

Copyright © 2015 William Labecca et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Bagley-Torvik equation appears in viscoelasticity problems where fractional derivatives seem to play an important role concerning empirical data. There are several works treating this equation by using numerical methods and analytic formulations. However, the analytical solutions presented in the literature consider particular cases of boundary and initial conditions, with inhomogeneous term often expressed in polynomial form. Here, by using Laplace transform methodology, the general inhomogeneous case is solved without restrictions in boundary and initial conditions. The generalized Mittag-Leffler functions with three parameters are used and the solutions presented are expressed in terms of Wiman’s functions and their derivatives.