Golmankhaneh, Alireza KhaliliIsayeva, Elmira2026-01-302026-01-3020260020-77481572-957510.1007/s10773-026-06250-3https://doi.org/10.1007/s10773-026-06250-3https://hdl.handle.net/20.500.14720/29658In this paper, we extend Nelson's stochastic mechanics to a fractal time framework using fractal calculus. By modeling quantum particle motion with fractal stochastic differential equations, we define forward, backward, and osmotic velocities and derive the fractal Fokker-Planck equation. Introducing a fractal complex wave function, we rigorously derive the fractal Schr & ouml;dinger equation, revealing how quantum behavior can emerge from stochastic dynamics in fractal time.eninfo:eu-repo/semantics/closedAccessFractal CalculusFractal Nelson's Stochastic MechanicsFractal Schrödinger EquationFractal Stochastic Differential EquationsArticle