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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]

We study interpolation spaces obtained via a general discrete interpolation method based on a Banach space with an unconditional basis. We find conditions which guarantee that such interpolation spaces have the Opial property and the uniform Opial property. [ABSTRACT FROM AUTHOR]

We study functional calculus properties of C0-groups on real interpolation spaces using transference principles. We obtain interpolation versions of the classical transference principle for bounded groups and of a recent transference principle for unbounded groups. Then we show that each group generator on a Banach space has a bounded -calculus on real interpolation spaces. Additional results are derived from this. [ABSTRACT FROM AUTHOR]