  The theory of derivatives and integrals of non-integer order goes back to
Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional
vector calculus (FVC) has only 10 years. The main approaches to formulate a
FVC, which are used in the physics during the past few years, will be briefly
described in this paper. We solve some problems of consistent formulations of
FVC by using a fractional generalization of the Fundamental Theorem of
Calculus. We define the differential and integral vector operations. The
fractional Green's, Stokes' and Gauss's theorems are formulated. The proofs of
these theorems are realized for simplest regions. A fractional generalization
of exterior differential calculus of differential forms is discussed.
Fractional nonlocal Maxwell's equations and the corresponding fractional wave
equations are considered.
