Fractional Kinetic Equations

We develop the idea of non-Markovian CTRW (continuous time random walk) approximation to evolution interacting particle systems, which leads a general class fractional kinetic measure-valued evolutions with variable order. prove well-posedness resulting new equations and present probabilistic formula for their solutions. Though our method are quite general, simplicity we treat in detail only versions diffusions. The paper can be considered as development ideas from works Belavkin Maslov devoted Markovian (quantum classical) systems particles.