The link between fractional and stochastic calculus established in part I of this paper is investigated in more detail. We study a fractional integral operator extending the Lebesgue–Stieltjes integral and introduce a related concept of stochastic integral which is similar to the so–called forward integral in stochastic integration theory. The results are applied to ODE driven by fractal functi...

Stochastic diffusion is a general phenomenon observed in various national and engineering systems. It is typically modeled by either stochastic differential equation (SDE) or Fokker-Planck equation (FPE), which are equivalent approaches. Path integral is an accurate and effective method to solve FPEs. Yet, computational efficiency is the common challenge for path integral and other numerical me...