Approximation of Fractional-Order Operators

  • Reyad El-KhazaliEmail author
  • Iqbal M. Batiha
  • Shaher Momani
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 303)


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.


Fractional-Order models Oustaloup’s approximation Matsuda’s approximation AbdelAty’s approximation El-Khazali’s approximation 



We thank the sponsors of the International Conference on Fractional Differentiation and its Applications (ICFDA 2018), who provided insight and expertise that greatly assisted the research to be in hand. We would also like to thank the international editors, Praveen Agarwal, Dumitru Baleanu, YangQuan Chen, and Tenreiro Machado, for their valuable comments and remarks.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Reyad El-Khazali
    • 1
    Email author
  • Iqbal M. Batiha
    • 2
  • Shaher Momani
    • 2
    • 3
  1. 1.ECSE DepartmentKhalifa UniversityAbu DhabiUAE
  2. 2.Department of MathematicsThe University of JordanAmmanJordan
  3. 3.Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of ScienceKing Abdulaziz UniversityJeddahKingdom of Saudi Arabia

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