  The maximal B_{p,q}^{s}-regularity properties of a nonlocal fractional
elliptic equation is studied. Particularly, it is proven that the operator
generated by this nonlocal ell{\i}p{\i}t{\i}c equation in B_{p,q}^{s} is
sectorial and also is a generator of an analytic semigroup. Moreover,
well-posedeness of nonlocal fractional parabolic equation in Besov spaces are
established.
