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 fractıonal differential equations and the system of nonlocal fractıonal differential equations are studied.

中文翻译：

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非局部分数阶微分方程及其应用

研究了Banach空间中非局部分数阶微分方程的正则性质。对于分数阶导数，抽象椭圆算子具有均匀的（（L_ {p} \））可分性和清晰的分解估计。特别地，已经证明，由这些方程生成的分数椭圆算子是扇形的，并且也是解析半群的生成器。此外，建立了非局部分数阶抽象抛物方程的最大正则性质。作为应用，研究了非局部各向异性分形微分方程和非局部分形微分方程组。