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In this paper we analyze fractional Fokker-Planck equation describingsubdiffusion in the general infinitely divisible (ID) setting. We show that inthe case of space-time-dependent drift and diffusion and time-dependent jumpcoefficient, the corresponding stochastic process can be obtained bysubordinating two-dimensional system of Langevin equations driven byappropriate Brownian and Levy noises. Our result solves the problem ofstochastic representation of subdiffusive Fokker-Planck dynamics in fullgenerality.

Stochastic representation of fractional subdiffusion equation. The case  of infinitely divisible waiting times, Levy noise and space-time-dependent  coefficients