Regularity properties of nonlocal fractional differential equations and applications

Shakhmurov V.

GEORGIAN MATHEMATICAL JOURNAL, vol.29, no.2, pp.275-284, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.1515/gmj-2021-2128
  • Journal Name: GEORGIAN MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.275-284
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

The regularity properties of nonlocal fractional elliptic and parabolic equations in vector-valued Besov spaces are studied. The uniform B-p,(q)s-separability properties and sharp resolvent estimates are obtained for abstract elliptic operator in terms of fractional derivatives. In particular, it is proven that the fractional elliptic operator generated by these equations is sectorial and also is a generator of an analytic semigroup. Moreover, the maximal regularity properties of the nonlocal fractional abstract parabolic equation are established. As an application, the nonlocal anisotropic fractional differential equations and the system of nonlocal fractional parabolic equations are studied.