  Boundary value problems for nonlocal fractional elliptic equations with
parameter in Banach spaces are studied. Uniform $L_p$-separability properties
and sharp resolvent estimates are obtained for elliptic equations in terms of
fractional derivatives. Particularly, it is proven that the fractional
ellipitic operator generated by these equations is sectorial and also is a
generator of an analytic semigroup. Moreover, maximal regularity properties of
nonlocal fractional abstract parabolic equation are established. As an
application, the nonlocal anisotropic fractional differential equations and the
system of nonlocal fractional differential equations are studied.
