On the Kolmogorov forward equations within Caputo and Riemann-Liouville fractions derivatives

In this work, we focus on the fractional versions of the well-known Kolmogorov forward equations. We consider the problem in two cases. In case 1, we apply the left Caputo fractional derivatives for α ∈ (0, 1] and in case 2, we use the right Riemann-Liouville fractional derivatives on R₊, for α ∈ (1, +∞). The exact solutions are obtained for the both cases by Laplace transforms and stable subordinators.