Stochastic Foundations of the Fractal Schrödinger Equation

Khalili Golmankhaneh A., Isayeva E.

International Journal of Theoretical Physics, cilt.65, sa.2, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 65 Sayı: 2
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1007/s10773-026-06250-3
  • Dergi Adı: International Journal of Theoretical Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, MathSciNet, zbMATH
  • Anahtar Kelimeler: Fractal calculus, Fractal Nelson’s stochastic mechanics, Fractal Schrödinger equation, Fractal stochastic differential equations
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In 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 Schrödinger equation, revealing how quantum behavior can emerge from stochastic dynamics in fractal time.