January 2001 - 010101
CISM chapter on Fractional Calculus by Gorenflo and Mainardi (to download)

We are pleased to offer to the interested visitor of the WEB site www.fracalmo.org  the possibility of down-loading the chapter by R. Gorenflo and F. Mainardi  "Fractional Calculus: Integral and Differential Equations of Fractional Order" appeared in the book "Fractals and Fractional Calculus  in Continuum Mechanics" edited by A. Carpinteri and F. Mainardi, Springer Verlag, New-York and Wien, 1997, pp. 223-276.
dowload the pdf file:  fmrg10.pdf (422 kb)
This chapter can be considered a concise course on Riemann-Liouville Fractional Calculus, which is suitable in treating time causal processes, i.e. processes governed by evolution integro-differential equations of fractional order with time t > 0. Furthermore, we have pointed out the key role of the Mittag-Leffler function by discussing some applications and presenting historical notes about it. This down-loadable version contains some light improvements and some up-dated references with respect to the original published version. In our chapter the references to the books and treatises on fractional calculus are till 1997: herewith we enclose the relevant and general references concerning fractional calculus appeared from 1998 to 2000:

- a new journal: Fractional Calculus and Applied Analysis
  Managing Editor  Virginia Kiryakova, has been published from 1998 with 4 issues per year.

- a new treatise (recommended for applied scientists and engineers):
  I. Podlubny, Fractional Differential Equations,
  Academic Press, San Diego, 1999, pp. 340.  vol 198  in Mathematics in Science and Engineering

- a new edited book (recommended for physicists):
  R. Hilfer (Editor), Applications of Fractional Calculus in Physics,
  World Scientific, Singapore, 2000, pp. 463

Soon we do hope to complete our lecture notes for the MaPhySto Center   (University of Aarhus)
R. Gorenflo and F. Mainardi, Fractional Diffusion Processes based on our lectures given  at the mini-course on Fractional Calculus held on January 24-28, 2000 (www.maphysto.dk/events/LevyCAC2000)