Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations

In this paper strong dissipativity of generalized time-fractional derivatives on Gelfand triples properly in time weighted L p -path spaces is proved. particular, as special cases the classical Caputo derivative and other fractional appearing applications are included. As a consequence one obtains existence uniqueness solutions to evolution equations with derivatives. These type d t ( k ? u ) + A , = f 0 < T (in general nonlinear) operators ? satisfying weak monotonicity conditions. Here non-increasing locally Lebesgue-integrable nonnegative function [ ? lim s ? . Analogous results for case, where replaced by additive noise, obtained well. Applications include quasi-linear (stochastic) partial differential equations. porous medium fast diffusion ordinary or Laplace -Laplace equation covered.