Space-time fractional Zener wave equation

Abstract

Space-time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analyzed. 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.

References in corpus (3)

• Some aspects of fractional diffusion equations of single and distributed order
• On a system of equations arising in viscoelasticity theory of fractional type
• Spatially fractional-order viscoelasticity, non-locality and a new kind of anisotropy

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