Regularity Properties of Solutions of Fractional Evolution Equations

In this paper we continue our work on regularity properties of solutions of fractional evolution equations. In particular, we study the equation 1 D t α ( u t − u 1 ) ( t ) + B u ( t ) = f ( t ) ,           u ( 0 ) = u 0 ,           t ≥ 0 , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187810/28005645-324c-4d25-a9e4-00a49a74dffd/content/eqn_chapter_19_1.tif"/> which is of order 1 + α. The function u is the unknown, taking values in a Banach space X; α ∈ (0, 1); u ₀, u ₁ and f are given, with u ₀, u ₁ ∈ X and f ∈ C ( [ 0 , T ] ; X ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187810/28005645-324c-4d25-a9e4-00a49a74dffd/content/inq_chapter19_235_1.tif"/> for some T > 0.