| Abstract: |
| In this talk we shall identify generalized time-fractional derivatives as generators of $C_0$-operator semigroups and prove their strong dissipativity on Gelfand triples of properly in time weighted $L^2$-path spaces.
In particular, the classical Caputo derivative is included as a special case.
As a consequence one obtains the existence and uniqueness of solutions to evolution equations on Gelfand triples with generalized time-fractional derivatives.
These equations are of type
\begin{equation*}
\frac{d}{dt} (k * u)(t) + A(t, u(t)) = f(t), \quad 0 |
|