The fractional calculus is the name for the theory of integrals and derivatives of arbitrary order, which generalize the notions of n‐fold integration and integer‐order differentiation.Differential equations of fractional order appear in certain applied problems and in theoretical researches. In this paper, the Euler‐Lagrange equations of the Lagrangians linear in velocities were derived using the fractional calculus. Two examples of constrained systems possessing a gauge invariance are investigated in details, the explicit solutions of Euler‐Lagrange equations are obtained, and the recovery of the classical results is discussed. © 2004 American Institute of Physics