  In this paper, we introduce a new classical fractional particle model
incorporating fractional first derivatives. This model represents a natural
extension of the standard classical particle with kinetic energy being
quadratic in fractional first derivatives and fractional linear momenta,
similarly to classical mechanics. We derive the corresponding equations of
motion and explore the symmetries of the model. Also, we present the
formulation in terms of fractional potentials. Two important examples are
analytically solved: the free particle and the particle subjected to
generalized forces characterized by fractional first derivatives.
