Cauchy problem for evolution equations of a fractional order

By Anatoly N. Kochubei, S. Eidelman. 2004

109 citations recorded by the source corpus.

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Citations in the corpus

Cauchy problem for fractional diffusion equations (2003, background): “1), in which B is a closed operator on a Banach space ([12, 8, 3, 4, 2], and others).”
On fractional Duhamel's principle and its applications (2010, background): “What concerns fractional order differential-operator equations, Kochubei [17] studied existence and uniqueness of a solution to the abstract Cauchy problem Dα∗ u(t) = Au(t), u(0) = u0, with Caputo-Djrbashian fractional derivative for 0 α 1 and a closed operator A with a dense domain D(A) in a Ba”
Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation (2011, unknown): “In the literature, mainly the initial-value problems for these equations were considered until now (see e.g. [9] [11] [14] [16] [25] [33] [40]).”
Distributed order calculus and equations of ultraslow diffusion (2007, methodology): “The mathematical theory was initiated independently by Schneider and Wyss [37] and the author [18,19]; for more recent developments see [9,10,15] and references therein.”
Time fractional equations and probabilistic representation (2017, background): “8); see [10, 11, 15] for cases of ∂ t u = Lu and [13] for distributed order time fractional equation ∂w t u = Lu where L is a one-dimensional differential operator in a bounded interval.”
Time-fractional derivatives in relaxation processes: a tutorial survey (2008, background): “Although there appeared several papers by different authors, including Caputo [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], Gorenflo et al. [55, 56, 57, 58], Kochubei [71, 72], Mainardi [78, 79, 80, 83], where the alternative derivative was adopted, it was mainly with the 1999 book by Po”
Overview to mathematical analysis for fractional diffusion equations - new mathematical aspects motivated by industrial collaboration (2010, methodology): “Kochubei [21], [22] applied the semigroup theory in Banach spaces, and Eidelman and Kochubei [8] constructed the fundamental solution in R and proved the maximum principle for the Cauchy problem.”
Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems (2011, methodology): “Kochubei [19,20] applied the semigroup theory in Banach spaces, and Eidelman and Kochubei [9] constructed the fundamental solution in Rd and proved the maximum principle for the Cauchy problem.”
Distributed-order fractional diffusions on bounded domains (2009, methodology): “See also the pioneering work of Kochubei [18,19].”