SOLUTION OF THE FUNDAMENTAL LINEAR FRACTIONAL ORDER DIFFERENTIAL EQUATION

A. Charef, M. Assabaa, Z. Santouh

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.

References

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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