Special Session 59:
 Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations}
 Michael Roeckner Bielefeld UniversityGermany Co-Author(s):    Wei Liu, Jose Luis da Silva
 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