On the fractal Langevin equation

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Khalili Golmankhaneh A.

Fractal and Fractional, cilt.3, sa.1, ss.1-9, 2019 (Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 3 Sayı: 1
  • Basım Tarihi: 2019
  • Doi Numarası: 10.3390/fractalfract3010011
  • Dergi Adı: Fractal and Fractional
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.1-9
  • Anahtar Kelimeler: Fractal Langevin equations, Fractal mean square displacement, Local fractal calculus, Middle-τ Cantor sets
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this paper, fractal stochastic Langevin equations are suggested, providing a mathematical model for random walks on the middle-τ Cantor set. The fractal mean square displacement of different random walks on the middle-τ Cantor set are presented. Fractal under-damped and over-damped Langevin equations, fractal scaled Brownian motion, and ultra-slow fractal scaled Brownian motion are suggested and the corresponding fractal mean square displacements are obtained. The results are plotted to show the details.