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 JAMP  Vol.6 No.1 , January 2018
Hölder Regularity for Abstract Fractional Cauchy Problems with Order in (0,1)
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).
Cite this paper: Li, C. and Li, M. (2018) Hölder Regularity for Abstract Fractional Cauchy Problems with Order in (0,1). Journal of Applied Mathematics and Physics, 6, 310-319. doi: 10.4236/jamp.2018.61030.
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