XXXVII SUMMER SCHOOL ON MATHEMATICAL PHYSICS
Ravello, Italy, September 17–29, 2012
Gruppo Nazionale per la Fisica Matematica
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]
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
Further reading
To appear here soon.