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- W4225659740 abstract "We consider generalized time-fractional evolution equations of the form $$u(t)=u_0+int_0^tk(t,s)Lu(s)ds$$ with a fairly general memory kernel $k$ and an operator $L$ being the generator of a strongly continuous semigroup. In particular, $L$ may be the generator $L_0$ of a Markov process $xi$ on some state space $Q$, or $L:=L_0+bnabla+V$ for a suitable potential $V$ and drift $b$, or $L$ generating subordinate semigroups or Schr{o}dinger type groups. This class of evolution equations includes in particular time- and space- fractional heat and Schrodinger type equations. We show that a subordination principle holds for such evolution equations and obtain Feynman-Kac formulae for solutions of these equations with the use of different stochastic processes, such as subordinate Markov processes and randomly scaled Gaussian processes. In particular, we obtain some Feynman-Kac formulae with generalized grey Brownian motion and other related self-similar processes with stationary increments." @default.
- W4225659740 created "2022-05-05" @default.
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- W4225659740 date "2022-08-19" @default.
- W4225659740 modified "2023-09-26" @default.
- W4225659740 title "Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations" @default.
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- W4225659740 doi "https://doi.org/10.1007/s13540-022-00082-8" @default.
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