2005/06/30 by Vasily E. Tarasov, VASILY E. TARASOV · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Action (physics) #Advanced Mathematical Theories and Applications #Fractal #Fractal derivative #Fractal dimension #Fractal dimension on networks #Fractional Differential Equations Solutions #Fractional calculus #Generalization #String (physics) #Thermoelastic and Magnetoelastic Phenomena #physics.class-ph
paper · pdf · doi:10.1142/s0217984905008712
published as Modern Physics Letters B. Vol.19. No.15. (2005) 721-728 · 8 pages, 2 figures, LaTeX
openalex publication_date 2005/06/30 · arxiv created 2006/04/29 · arxiv updated 2015/03/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We use the fractional integrals to describe fractal solid. We suggest to consider the fractal solid as special (fractional) continuous medium. We replace the fractal solid with fractal mass dimension by some continuous model that is described by fractional integrals. The fractional integrals are considered as approximation of the integrals on fractals. We derive fractional generalization of the action functional and the Euler–Lagrange equation for the fractal solid string. The solution of wave equation for fractal solid string is considered.