Hölder Regularity for Abstract Fractional Cauchy Problems with Order in (0,1)
نویسندگان
چکیده
In this paper, we study the regularity of mild solution for the following fractional abstract Cauchy problem ( ) ( ) ( ), (0, ] t D u t Au t f t t T α = + ∈ (0) u = 0 x on a Banach space X with order (0,1) α ∈ , 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 ([0, ]; ) p f L T X ∈ for some 1/ p α > , then the mild solution to the above equation is in 1/ [ , ] p C T α− for every 0 > . Moreover, if f is Hölder continuous, then so are the ( ) t D u t α and ( ) Au t .
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