Nonlocal Fractional Differential Equations and Applications

Abstract

The regularity properties of nonlocal fractional differential equations in Banach spaces are studied. Uniform $$L_{p}$$ -separability properties and sharp resolvent estimates are obtained for abstract elliptic operator in terms of fractional derivatives. Particularly, it is proven that the fractional elliptic 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.