Waves in fractional Zener type viscoelastic media

DOI10.1016/j.jmaa.2009.10.043zbMath1185.35280arXiv1101.2966OpenAlexW2005259635MaRDI QIDQ847774

Ljubica Oparnica, Sanja Konjik, Dusan Zorica

Publication date: 19 February 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.2966

zbMATH Keywords

fractional derivativesfundamental solutionLaplace and Fourier transformsfractional Zener model

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Fundamental solutions to PDEs (35A08) Fractional derivatives and integrals (26A33) Transform methods (e.g., integral transforms) applied to PDEs (35A22) PDEs in connection with mechanics of deformable solids (35Q74)

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Cites Work

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• Some aspects of fractional diffusion equations of single and distributed order
• Fractals and fractional calculus in continuum mechanics
• A modified Zener model of a viscoelastic body
• Distributed order calculus and equations of ultraslow diffusion
• A diffusion wave equation with two fractional derivatives of different order
• A new dissipation model based on memory mechanism
• Time distributed-order diffusion-wave equation. I. Volterra-type equation
• Time distributed-order diffusion-wave equation. II. Applications of Laplace and Fourier transformations
• Multi–dimensional solutions of space–time–fractional diffusion equations
• Multidimensional solutions of time-fractional diffusion-wave equations
• Nonstationary Rayleigh waves on the thermally-insulated surfaces of some thermoelastic bodies of revolution