Fractional Calculus, Some Basic Problems in Continuum and Statistical Mechanics.pdf

CISM LECTURE NOTES
International Centre for Mechanical Sciences
Palazzo del Torso, Piazza Garibaldi, Udine, Italy
FRACTIONAL CALCULUS :
Some Basic Problems in Continuum and Statistical Mechanics
Francesco MAINARDI
Department of Physics, University of Bologna
Via Irnerio 46, I-40126 Bologna, Italy
e-mail: ******@
TEX PRE-PRINT 58 pages : pp. 291-348
ABSTRACT..........................
1. LINEAR VISCOELASTICITY AND FRACTIONAL CALCULUS . . p. 292
2. THE BASSET PROBLEM VIA FRACTIONAL CALCULUS . . . . p. 303
3. BROWNIAN MOTION AND FRACTIONAL CALCULUS . . . . . p. 311
-WAVEEQUATION.......
APPENDIX: THE WRIGHT FUNCTION . . . . . . . . . . . . p. 333
REFERENCES........................
The paper is based on the lectures delivered by the author at the CISM Course
Scaling Laws and Fractality in Continuum Mechanics: A Survey of the Methods based
on Renormalization Group and Fractional Calculus, held at the seat of CISM, Udine,
from 23 to 27 September 1996, under the direction of Professors A. Carpinteri and
F. Mainardi.
This TEX pre-print is a revised version (November 2001) of the chapter published in
A. Carpinteri and F. Mainardi (Editors): Fractals and Fractional Calculus
in Continuum Mechanics, Springer Verlag, Wien and New York 1997, pp.
291-348.
Such book is the volume No. 378 of the series CISM COURSES AND LECTURES
[ISBN 3-211-82913-X]
i
PREFACE to the REVISED VERSION
In this revised version a number of misprints have been corrected and several
improvements have been introduced. All the plots have been re-drawn by using the
MATLAB system; for this the Author is grateful to his students: D. Moretti, G.
Pagnini, P. Paradisi, D. Piazza and D. Turrini. Up to some extent the references
have been up-dated. For further information about the applications of fractional
calculus we mend the recent treatises
– R. Hilfer (Editor): Applications of Fractional Calculus in Physic