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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Chen, Xi / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

IMPACT FACTOR 2017: 1.162

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Volume 19, Issue 3-4


A Robust Algorithm for Nonlinear Variable-Order Fractional Control Systems with Delay

José António Tenreiro Machado
  • Department of Electrical Engineering, Institute of Engineering, Rua Dr. António Bernardino de Almeida, 431, Porto 4249-015, Portugal
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Behrouz Parsa Moghaddam
Published Online: 2018-03-14 | DOI: https://doi.org/10.1515/ijnsns-2016-0094


In this paper, we propose a high-accuracy linear B-spline finite-difference approximation for variable-order (VO) derivative. We consider VO fractional differentiation as a control parameter for improving the stability in systems exhibiting vibrations. The method is applied to nonlinear feedback with VO fractional derivative. The results demonstrate the efficiency and high accuracy of the novel algorithm.

Keywords: variable-order fractional calculus; fractional calculus; finite-difference method; B-spline; feedback; nonlinear control systems

PACS: 02.70.Bf; 05.45.Pq; 05.45.Gg; 02.30.Ks


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About the article

Received: 2016-07-08

Accepted: 2018-02-04

Published Online: 2018-03-14

Published in Print: 2018-06-26

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 3-4, Pages 231–238, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2016-0094.

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