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

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