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Миникурс лаб Чебышева: Enzo Orsingher, "Fractional calculus and applications to stochastic processes"
by Egor Pifagorov - Monday, 12 March 2012, 08:34 PM
Fractional calculus and applications to stochastic processes

24.03, 26.03, 28.03, 31.03, 02.04, 04.04
17-00, 14-ая линия, ауд. 14 (в первый раз!)


1. Introduction to fractional calculus

The Riemann-Liouville integral.
The Riemann-Liouville derivative.
Relationship between fractional derivative and fractional integral and
between fractional integral and fractional derivative.
The Marchaud derivative.
Laplace transform of fractional derivative.
Dzhrbashyan-Caputo derivative.
Laplace transform of the Dzhrbashyan-Caputo derivative.

2. Fractional diffusion equation

Mittag-Leffler function.
Wright functions.
Solution of the fractional di usion equation.

3. Riesz calculus

The Riesz integral.
The Riesz derivative.
Space-fractional equation and stable processes.

4. Fractional Poisson process

Construction and distribution.
Time-fractional Poisson process as a renewal process.

5. Fractional pure birth process: non-linear and linear case

6. Fractional telegraph equation: solution and discussion

Some time will be devoted at the beginnig to the most important results
on Gamma function.