2010/08/24 by Renat T. Sibatov, Sibatov, Renat T., D. V. Uchaikin +2
Engineering · Mathematics · Physics and Astronomy · #Acoustic Wave Phenomena Research #FOS: Physical sciences #Fractional Differential Equations Solutions #Numerical methods in engineering #Other Condensed Matter (cond-mat.other) #cond-mat.other
paper · pdf · doi:10.48550/arxiv.1008.3972
5 pages, 4 figures, presented at Int. Conf. "New Trends in Nanotechnology and Dynamical Systems - 2010" (Turkey, Ankara)
arxiv created 2010/08/24 · openalex publication_date 2010/08/24 · arxiv updated 2010/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A fractional relaxation equation in dielectrics with response function of the Havriliak-Negami type is derived. An explicit expression for the fractional operator in this equation is obtained and Monte Carlo algorithm for calculation of action of this operator is constructed. Relaxation functions calculated numerically according to this scheme coincide with analytical functions obtained earlier by other authors. The algorithm represents a numerical way of calculation in relaxation problems with arbitrary initial and boundary conditions. A fractional equation for electromagnetic waves in such dielectric media is obtained. Numerical results are in a good agreement with experimental data.