In fractional Brownian motion, the Fokker-Planck equation is given by,
$$ \frac{\partial p(x,t)}{\partial t} = 2D_{2H}Ht^{2H-1}\frac{\partial^2 p(x,t)}{\partial x^2} $$
I wish to take the Laplace transform of this equation in time-domain, but I am stuck with the product of two functions on the RHS, which is $$ \mathscr{L}\big\{t^{2H-1}p(x,t)\big\} $$
Any thoughts on how to write this as a Laplace transform of $p(x,t)$, what kind of functions can be adopted to calculate this Laplace transform (in terms of Fox functions or Mittag-Leffler functions etc.)