Fractional backward Kolmogorov equations

This paper derives the fractional backward Kolmogorov equations in fractal space-time based on the construction of a model for dynamic trajectories. It shows that for the type of fractional backward Kolmogorov equation in the fractal time whose coefficient functions are independent of time, its solution is equal to the transfer probability density function of the subordinated process X (S-alpha(t)), the subordinator S-alpha(t) is termed as the inverse-time alpha-stable subordinator and the process X (tau) satisfies the corresponding time homogeneous Ito stochastic differential equation.