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Novel interpolation spaces and maximal‐weighted Hölder regularity results for the fractional abstract Cauchy problem.
- Source :
-
Mathematische Nachrichten . Feb2024, Vol. 297 Issue 2, p560-576. 17p. - Publication Year :
- 2024
-
Abstract
- In this paper, the maximal‐weighted Hölder regularity for the fractional abstract Cauchy problem is presented. First, two classes of novel interpolation spaces constructed by resolvent families are portrayed. Afterward, by applying the resolvent method and the properties of interpolation spaces, the maximal‐weighted Hölder regularity of the mild solution is established in weighted Hölder space C0β,γ(X)$C_0^{\beta ,\gamma }(X)$ (0≤γ≤β$0\le \gamma \le \beta$, 0<β<1$0<\beta <1$). Eventually, an instance for the fractional differential equation of 2m‐order multidimensional parabolic type is provided to verify the reasonability of main conclusions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0025584X
- Volume :
- 297
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Mathematische Nachrichten
- Publication Type :
- Academic Journal
- Accession number :
- 175364878
- Full Text :
- https://doi.org/10.1002/mana.202300093