Applications of fractional calculus in mechanics. (English) Zbl 1113.26303
Rusev, P. (ed.) et al., Transform methods and special functions. Proceedings of the 2nd international workshop, Varna, Bulgaria, August 23–30, 1996. Sofia: Bulgarian Academy of Sciences, Institute of Mathematics and Informatics (ISBN 954-8986-05-1/pbk). 309-334 (1998).
Summary: In this survey paper we review some applications of the Riemann-Liouville fractional calculus developed by the author (partly in collaboration with others) to treat some basic problems in mechanics. These problems concern relaxation and oscillation phenomena, mathematical modelling of viscoelastic bodies, and unsteady motion of a particle in a viscous fluid, including random Brownian motion. Our analysis, carried out using the Laplace transform, exhibits the key role played by the Mittag-Leffler function.
For the entire collection see [Zbl 0914.00065].
For the entire collection see [Zbl 0914.00065].
MSC:
| 26A33 | Fractional derivatives and integrals |
| 33E20 | Other functions defined by series and integrals |
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
| 70J99 | Linear vibration theory |
