Nonlocal fractional elliptic and parabol{\i}c equat{\i}ons in Besov spaces and applications

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.