The construction of solutions for some model problem classes with resolvent equations of a fractional order
https://doi.org/10.29235/1561-2430-2022-58-1-60-70
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.
About the Authors
M. A. Zhuravkov
Belarusian State University
Belarus
Belarus
Michael A. Zhuravkov – Dr. Sc. (Physics and Mathematics), Professor, Head of the Department of Theoretical and Applied Mechanics
9, Bobruiskaya Str., 220030, Minsk
V. V. Kolyachko
Belarusian State University
Belarus
Belarus
Vladislav V. Kolyachko – Assistant of Laboratory of Applied Mechanics, Theoretical and Applied Mechanics Department
9, Bobruiskaya Str., 220030, Minsk
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