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Clément, P., Gripenberg, G. and Londen, S-O. (2000) Schauder Estimates for Equations with Fractional Derivatives. Trans. Amer. Math. Soc., 352, 2239-2260.

has been cited by the following article:

• TITLE: Hölder Regularity for Abstract Fractional Cauchy Problems with Order in (0,1)

  AUTHORS: Chenyu Li, Miao Li

  KEYWORDS: Fractional Cauchy Problem, Fractional Resolvent Family, Generator, Regularity, Hölder Continuity

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.6 No.1, January 31, 2018

  ABSTRACT: In this paper, we study the regularity of mild solution for the following fractional abstract Cauchy problem Dt αu(t)=Au(t)+f(t), t ∈ (0,T] u(0)= x0 on a Banach space X with order α ∈ (0,1), where the fractional derivative is understood in the sense of Caputo fractional derivatives. We show that if A generates an analytic α-times resolvent family on X and f ∈ Lp ([0,T];X) for some p > 1/α, then the mild solution to the above equation is in Cα-1/p[ò,T] for every ò > 0. Moreover, if f is Hölder continuous, then so are the Dt αu(t) and Au(t).