Well-posedness for time-fractional evolution equations by the Yosida approximation

We consider an initial value problem for a time-fractional evolution equation in a Hilbert space $X$: $$ \partial_t^α (u(t)-a) = Au(t) \qquad \mbox{for $0<t<T$}, $$ where $\partial_t^α$ denotes a fractional differential operator of Caputo type with order $0<α<1,$ $u\colon (0,T) \to X,$ $a$ describes