  In the present work we redefine and generalize the action principle for
dissipative systems proposed by Riewe by fixing the mathematical
inconsistencies present in the original approach. In order to formulate a
quadratic Lagrangian for non-conservative systems, the Lagrangian functions
proposed depend on mixed integer order and fractional order derivatives. As
examples, we formulate a quadratic Lagrangian for a particle under a frictional
force proportional to the velocity, and to the classical problem of an
accelerated point charge.
