Fractional Abstract Differential Equations and Applications

Boundary value problems for 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 elliptic operators generated by these equations are positive and also are generators of the analytic semigroups. Moreover, maximal regularity properties of the fractional abstract parabolic equation are established. As an application, the parameter-dependent anisotropic fractional differential equations and the system of fractional differential equations are studied.