Nonlocal Fractional Differential Equations and Applications
Complex Analysis and Operator Theory, vol.14, no.4, 2020 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 14 Issue: 4
- Publication Date: 2020
- Doi Number: 10.1007/s11785-020-01006-1
- Journal Name: Complex Analysis and Operator Theory
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Keywords: Abstract differential equations, Abstract parabolic equations, Fractional-differential equations, Maximal Lp regularity, Operator-valued multipliers, Sobolev-Lions spaces
- Open Archive Collection: Article
- Azerbaijan State University of Economics (UNEC) Affiliated: Yes
Abstract
The regularity properties of nonlocal fractional differential equations in Banach spaces are studied. Uniform Lp-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.