  The aim of this paper is to present a simple generalization of bosonic string
theory in the framework of the theory of fractional variational problems.
Specifically, we present a fractional extension of the Polyakov action, for
which we compute the general form of the equations of motion and discuss the
connection between the new fractional action and a generalization the
Nambu-Goto action. Consequently, we analyse the symmetries of the modified
Polyakov action and try to fix the gauge, following the classical procedures.
Then we solve the equations of motion in a simplified setting. Finally, we
present an Hamiltonian description of the classical fractional bosonic string
and introduce the fractional light-cone gauge. It is important to remark that,
throughout the whole paper, we thoroughly discuss how to recover the known
results as an "integer" limit of the presented model.
