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Space-time fractional Zener wave equation
T M Atanackovic1, M Janev2, Lj Oparnica3
1Department of Mechanics, Faculty of Technical Sciences , University of Novi Sad , Trg D. Obradovica 6, 21000 Novi Sad, Serbia.
Proceedings. Mathematical, Physical, and Engineering Sciences
|February 10, 2015
Summary
This study analyzes the space-time fractional Zener wave equation for viscoelastic materials. The research proves the existence and uniqueness of solutions, offering insights into wave propagation and non-propagating disturbances.
Area of Science:
- Continuum Mechanics
- Viscoelasticity
- Wave Propagation
Background:
- Viscoelastic materials exhibit complex behaviors under stress.
- Fractional calculus offers advanced modeling for materials with memory effects.
- The Zener model is a foundational concept in viscoelasticity.
Purpose of the Study:
- To derive and analyze the space-time fractional Zener wave equation.
- To investigate wave propagation and non-propagating disturbances in fractional viscoelasticity.
- To establish the mathematical foundation for solutions to this generalized model.
Main Methods:
- Derivation of the space-time fractional Zener wave equation.
- Mathematical analysis of the generalized Cauchy problem.
- Proof of existence and uniqueness of solutions.
- Investigation of special cases and numerical simulations.
Main Results:
- The space-time fractional Zener wave equation accurately models viscoelastic materials.
- The model accommodates both finite-speed waves and non-propagating disturbances.
- Existence and uniqueness of solutions for the generalized Cauchy problem are rigorously demonstrated.
Conclusions:
- The derived fractional Zener wave equation provides a robust framework for analyzing complex viscoelastic phenomena.
- The mathematical proofs confirm the reliability of the model for predicting wave behavior.
- Numerical examples illustrate the practical applicability of the theoretical findings.
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