Fractal calculus approach to diffusion on fractal combs

Khalili Golmankhaneh A., Ontiveros L. A. O.

Chaos, Solitons and Fractals, cilt.175, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 175
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1016/j.chaos.2023.114021
  • Dergi Adı: Chaos, Solitons and Fractals
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Compendex, INSPEC, zbMATH
  • Anahtar Kelimeler: Fractal calculus, Fractal delay differential equations, Fractal retarded delay differential equations, Neutral delay differential equations
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this paper, we present a generalization of diffusion on fractal combs using fractal calculus. We introduce the concept of a fractal comb and its associated staircase function. To handle functions supported on these combs, we define derivatives and integrals using the staircase function. We then derive the Fokker–Planck equation for a fractal comb with dimension α, incorporating fractal time, and provide its solution. Additionally, we explore α-dimensional and (2α)-dimensional Brownian motion on fractal combs with drift and fractal time. We calculate the corresponding fractal mean square displacement for these processes. Furthermore, we propose and solve the heat equation on an α-dimensional fractal comb space. To illustrate our findings, we include graphs that showcase the specific details and outcomes of our results.