On maximal regularity and semivariation of $\alpha$-times resolvent families

Fu-Bo Li, Miao Li

Let $1<\alpha <2$ and $A$ be the generator of an $\alpha$-times resolvent family $\{S_{\alpha }(t){\}}_{t\ge 0}$ on a Banach space $X$. It is shown that the fractional Cauchy problem ${\bf D}_t^αu(t)…