Geodesic
Fractional Kinetic Equations
Matematičeskie zametki, Tome 112 (2022) no. 4, pp. 567-585

Voir la notice de l'article provenant de la source Math-Net.Ru

We develop the idea of non-Markovian CTRW (continuous time random walk) approximation to the evolution of interacting particle systems, which leads to a general class of fractional kinetic measure-valued evolutions with variable order. We prove the well-posedness of the resulting new equations and present a probabilistic formula for their solutions. Though our method are quite general, for simplicity we treat in detail only the fractional versions of the interacting diffusions. The paper can be considered as a development of the ideas from the works of Belavkin and Maslov devoted to Markovian (quantum and classical) systems of interacting particles.
Keywords: fractional kinetic equations, interacting particles, fractional derivative of variable order, continuous time random walks (CTRW). 
@article{MZM_2022_112_4_a6,
     author = {V. N. Kolokoltsov and M. S. Troeva},
     title = {Fractional {Kinetic} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {567--585},
     publisher = {mathdoc},
     volume = {112},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_4_a6/}
}
TY  - JOUR
AU  - V. N. Kolokoltsov
AU  - M. S. Troeva
TI  - Fractional Kinetic Equations
JO  - Matematičeskie zametki
PY  - 2022
SP  - 567
EP  - 585
VL  - 112
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2022_112_4_a6/
LA  - ru
ID  - MZM_2022_112_4_a6
ER  - 
%0 Journal Article
%A V. N. Kolokoltsov
%A M. S. Troeva
%T Fractional Kinetic Equations
%J Matematičeskie zametki
%D 2022
%P 567-585
%V 112
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2022_112_4_a6/
%G ru
%F MZM_2022_112_4_a6
V. N. Kolokoltsov; M. S. Troeva. Fractional Kinetic Equations. Matematičeskie zametki, Tome 112 (2022) no. 4, pp. 567-585. http://geodesic.mathdoc.fr/item/MZM_2022_112_4_a6/