XXXVII SUMMER SCHOOL ON MATHEMATICAL PHYSICS
Ravello, Italy, September 17–29, 2012
Gruppo Nazionale per la Fisica Matematica

Photos of the lecturers of the second week Photo of lecturers of the second week with participants. Photos of the lecturers of the second week

Fractional Calculus: Methods for Applications

Lectures by Professor Igor Podlubny,
BERG Faculty, Technical University of Kosice, Slovakia
September 24–29, 2012, daily at 10:00–11:00

Lecture 1:
Introduction. Interpretations of fractional-order operators and initial conditions for fractional differential equations.
[slides] [video]
Lecture 2:
Direct approaches to numerical fractional differentiation and to numerical solution of fractional differential equations. "Short memory" principle.
[slides] [video]
Lecture 3:
Matrix approach to numerical fractional differentiation and integration. Numerical solution of ordinary and partial fractional differential equations.
[slides] [video]
Lecture 4:
Matrix approach extended: distributed orders, non-equidistant grids, method of "large steps".
[slides] [video]
Lecture 5:
Building fractional-order models: Fitting experimental data using the Mittag-Leffler function.
[slides] [video]
Lecture 6:
Least circles versus least squares. Application to modeling economical processes. Available software.
[slides] [video]

Lecture notes

Draft version of October 02, 2012 is available.

Matlab software

Podlubny I., Kacenak M.: Mittag-Leffler function. Matlab Central File Exchange, #8738
Chen YQ: Generalized Mittag-Leffler function. Matlab Central File Exchange, #21454
Podlubny I.: Fitting data using the Mittag-Leffler function. Matlab Central File Exchange, #32170
Chen YQ: Oustaloup-Recursive-Approximation for Fractional Order Differentiators. Matlab Central File Exchange, #3802
Petras I.: Digital Fractional Order Differentiator/integrator - FIR type. Matlab Central File Exchange, #3673
Petras I.: Digital fractional-order differentiator and integrator - new IIR type. Matlab Central File Exchange, #31358
Valerio D.: Variable order derivatives. Matlab Central File Exchange, #24444
Petras I.: Fractional Order Chaotic Systems. Matlab Central File Exchange, #27336
Podlubny I., Skorvanek T., Vinagre B.: Matrix approach to discretization of ODEs and PDEs of arbitrary real order. Matlab Central File Exchange, #22071
Podlubny I.: Matrix approach to distributed-order ODEs and PDEs. Matlab Central File Exchange, #36570
Garrappa R.: Predictor-corrector PECE method for fractional differential equations. Matlab Central File Exchange, #32918
Petras I., Podlubny I.: Orthogonal Linear Regression in 3D-space by using Principal Components Analysis. Matlab Central File Exchange, #12395
Petras I., Bednarova D., Skovranek T., Podlubny I.: Total Least Squares Method. Matlab Central File Exchange, #31109
Podlubny I.: Require FEX package. Matlab Central File Exchange, #31069