Qualitative properties of fractional convolution elliptic and parabolic operators in Besov spaces

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Shakhmurov V., Shahmurov R.

FRACTIONAL CALCULUS AND APPLIED ANALYSIS, vol.27, no.4, pp.1579-1595, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 4
  • Publication Date: 2024
  • Doi Number: 10.1007/s13540-024-00302-3
  • Journal Name: FRACTIONAL CALCULUS AND APPLIED ANALYSIS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.1579-1595
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

The maximal B-p,q(s)-regularity properties of a fractional convolution elliptic equation is studied. Particularly, it is proven that the operator generated by this nonlocal elliptic equation is sectorial in B-p,q(s) and also is a generator of an analytic semigroup. Moreover, well-posedeness of nonlocal fractional parabolic equation in Besov spaces is obtained. Then by using the B-p,q(s)-regularity properties of linear problem, the existence, uniqueness of maximal regular solution of corresponding fractional nonlinear equation is established.