Space–time fractional Zener wave equation

2014/02/20 by Teodor M. Atanackovic, Teodor M. Atanacković, Marko Janev +5 · 18 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Computer science #Fractional Differential Equations Solutions #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Physics #Quantum mechanics #Space (punctuation) #Wave equation #Zener diode #math-ph #math.MP

paper · pdf · doi:10.1098/rspa.2014.0614

published in Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences 471(2174), 20140614 (Royal Society)

arxiv created 2014/02/20 · openalex publication_date 2014/12/24 · arxiv updated 2014/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The space-time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analysed. This model includes waves with finite speed, as well as non-propagating disturbances. The existence and the uniqueness of the solution to the generalized Cauchy problem are proved. Special cases are investigated and numerical examples are presented.

Citations

• On a fractional Zener elastic wave equation
• Application of Fractional Calculus for Dynamic Problems of Solid Mechanics: Novel Trends and Recent Results
• Some aspects of fractional diffusion equations of single and distributed order
• Nonlocal Continuum Field Theories
• Fractional Differential Equations
• Fractional Calculus and Waves in Linear Viscoelasticity