Abstract
In this paper, we represent new examples of constructing model problems of the mechanics of a deformable solid using a fractional differentiation apparatus. The solutions to boundary problems of mechanics are found, in which the defining differential equations have a fractional order. In particular, such problems as a model of a “fractal” oscillator, a model problem on the dynamic of wave propagation in rock, model problems on the deformation of wave propagation in deformable viscoelastic media (a semi-infinite viscoelastic rod) for various viscoelasticity models are considered. When building the solutions, the Mainardi algorithm and the Laplace transformation are used. Model solutions for the considered problems are built. Asymptotic solutions of wave propagation equations in viscoelastic media under different viscoelasticity models are obtained.
| Original language | English |
|---|---|
| Pages (from-to) | 60-70 |
| Number of pages | 11 |
| Journal | Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series |
| Volume | 58 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2022 |
| Externally published | Yes |
Keywords
- Laplace transform
- Mainardi algorithm
- fractal oscillator model
- fractional Caputo derivative
- fractional derivative of Riemann – Liouville
- fractional viscoelasticity models
- wave fractal equation of geomechanics
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