SOLUTION OF THE FUNDAMENTAL LINEAR FRACTIONAL ORDER DIFFERENTIAL EQUATION

A. Charef, M. Assabaa, Z. Santouh

2007

Abstract

This paper provides a solution of the fractional order system represented by the fundamental linear fractional order differential equation, namely, (τ0)m x((dm x(t))/(dtm)) + x(t) = e(t) whose transfer function is given by G(s)=(X(s)/(E(s)) = 1/[1+(τ0s)m] for 0 < m < 2. Simple methods of approximation, for a given frequency band, of the transfer function of this fractional order system by a rational function are presented. Analytical impulse and step responses of this system are derived. Illustrative examples are presented to show the exactitude of the approximation methods.

Paper Citation

in Harvard Style

Charef A., Assabaa M. and Santouh Z. (2007). SOLUTION OF THE FUNDAMENTAL LINEAR FRACTIONAL ORDER DIFFERENTIAL EQUATION . In Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 3: Fractional Order Systems, (ICINCO 2007) ISBN 978-972-8865-84-9, pages 407-413. DOI: 10.5220/0001634004070413

in Bibtex Style

@conference{fractional order systems07,
author={A. Charef and M. Assabaa and Z. Santouh},
title={SOLUTION OF THE FUNDAMENTAL LINEAR FRACTIONAL ORDER DIFFERENTIAL EQUATION},
booktitle={Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 3: Fractional Order Systems, (ICINCO 2007)},
year={2007},
pages={407-413},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001634004070413},
isbn={978-972-8865-84-9},
}

in EndNote Style

TY - CONF
JO - Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 3: Fractional Order Systems, (ICINCO 2007)
TI - SOLUTION OF THE FUNDAMENTAL LINEAR FRACTIONAL ORDER DIFFERENTIAL EQUATION
SN - 978-972-8865-84-9
AU - Charef A.
AU - Assabaa M.
AU - Santouh Z.
PY - 2007
SP - 407
EP - 413
DO - 10.5220/0001634004070413