Fractal calculus approach to diffusion on fractal combs

Alireza Khalili Golmankhaneh and Lilián Aurora Ochoa Ontiveros

Chaos, Solitons & Fractals, 2023, vol. 175, issue P1

Abstract: 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.

Keywords: Fractal comb; Fractal calculus; Combs’ staircase function; Mean square displacement; Diffusion on fractal (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923009220

DOI: 10.1016/j.chaos.2023.114021

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