Simulation method of fractional systems based on the discrete-time approximation of the Caputo fractional derivatives

Author

Aoun, M. ; Amairi, M. ; Najar, S. ; Abdelkrim, M.N.

Author_Institution

Nat. Eng. Sch. of Gabes (ENIG), Univ. of Gabes, Gabes, Tunisia

fYear

2011

fDate

22-25 March 2011

Firstpage

1

Lastpage

6

Abstract

This paper proposes a new method for the simulation of the fractional systems. It deals with the approximation methods of the fractional derivative. It compare the approximation based on Grünwald with Caputo approximation. The efficiency of each approximation methods in terms of execution time and quadratic error is evaluated for different differential orders and stepsize. The best approximation method is used to develop an original simulation method to demonstrate its effectiveness.

Keywords

approximation theory; differential equations; differentiation; Caputo approximation; Caputo fractional derivatives; Grünwald approximation; discrete-time approximation; execution time; fractional systems; quadratic error; simulation method; Analytical models; Approximation methods; Computational modeling; Mathematical model; Numerical models; Transfer functions; ACFDR; CFDR; Diethelm´s approximation; Fractional derivative; fractional systems; recursive pole-zero distribution; simulation;

fLanguage

English

Publisher

ieee

Conference_Titel

Systems, Signals and Devices (SSD), 2011 8th International Multi-Conference on

Conference_Location

Sousse

Print_ISBN

978-1-4577-0413-0

Type

conf

DOI

10.1109/SSD.2011.5767414

Filename

5767414