TY - GEN
T1 - Approximation of Fractional-Order Operators
AU - El-Khazali, Reyad
AU - Batiha, Iqbal M.
AU - Momani, Shaher
N1 - Publisher Copyright:
© 2019, Springer Nature Singapore Pte Ltd.
PY - 2019
Y1 - 2019
N2 - In order to deal with some difficult problems in fractional-order systems, like computing analytical time responses such as unit impulse and step responses; some rational approximations for the fractional-order operators are presented with satisfying results in simulation and realization. In this chapter, several comparisons in the time response and Bode results between four well-known methods; Oustaloup’s method, Matsuda’s method, AbdelAty’s method, and El-Khazali’s method are made for the rational approximation of fractional-order operator (fractional Laplace operator). The various methods along with their advantages and limitations are described in this chapter. Simulation results are shown for different orders of the fractional operator. It has been shown in several numerical examples that the El-Khazali’s method is very successful in comparison with Oustaloup’s, Matsuda’s, and AbdelAty’s methods.
AB - In order to deal with some difficult problems in fractional-order systems, like computing analytical time responses such as unit impulse and step responses; some rational approximations for the fractional-order operators are presented with satisfying results in simulation and realization. In this chapter, several comparisons in the time response and Bode results between four well-known methods; Oustaloup’s method, Matsuda’s method, AbdelAty’s method, and El-Khazali’s method are made for the rational approximation of fractional-order operator (fractional Laplace operator). The various methods along with their advantages and limitations are described in this chapter. Simulation results are shown for different orders of the fractional operator. It has been shown in several numerical examples that the El-Khazali’s method is very successful in comparison with Oustaloup’s, Matsuda’s, and AbdelAty’s methods.
KW - AbdelAty’s approximation
KW - El-Khazali’s approximation
KW - Fractional-Order models
KW - Matsuda’s approximation
KW - Oustaloup’s approximation
UR - http://www.scopus.com/inward/record.url?scp=85076741344&partnerID=8YFLogxK
U2 - 10.1007/978-981-15-0430-3_8
DO - 10.1007/978-981-15-0430-3_8
M3 - Conference contribution
AN - SCOPUS:85076741344
SN - 9789811504297
T3 - Springer Proceedings in Mathematics and Statistics
SP - 121
EP - 151
BT - Fractional Calculus - ICFDA 2018
A2 - Agarwal, Praveen
A2 - Agarwal, Praveen
A2 - Agarwal, Praveen
A2 - Baleanu, Dumitru
A2 - Chen, YangQuan
A2 - Momani, Shaher
A2 - Machado, José António Tenreiro
PB - Springer
T2 - International Conference on Fractional Differentiation and its Applications, ICFDA 2018
Y2 - 16 July 2018 through 18 July 2018
ER -