  A fractional variational principle was derived in order to be used with
lagrangians containing fractional derivatives of order 1/2. By forcing the
action associated to this type of lagrangian to be stationary, a modified
fractional Euler-Lagrange equation was obtained. This was shown to reproduce
the equations of motion of two basic 1-dimensional energy-dissipative systems:
a spring-mass system damped by friction, and a RLC circuit connected in series.
Finally, by using the fractional Euler-Lagrange equation, the Drude
relationship for electrons in metals was recovered when a fractional kinetic
energy was taken into consideration in the electron's associated energies.
