Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations

Abstract We consider a class of generalized time-fractional evolution equations containing fairly general memory kernel k and an operator L being the generator strongly continuous semigroup. show that subordination principle holds for such obtain Feynman-Kac formulae solutions these with use different stochastic processes, as subordinate Markov processes randomly scaled Gaussian processes. In particular, we some grey Brownian motion other related self-similar stationary increments.