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Equivalent Same-Order System for Multi-Rational-Order Fractional Differential System With Caputo Derivative

[+] Author Affiliations
Changpin Li

Shanghai University, Shanghai, China

Fengrong Zhang

Shanghai University, Shanghai; China University of Petroleum (East China), Qingdao, China

Paper No. DETC2011-47204, pp. 105-114; 10 pages
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 3: 2011 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5480-8
  • Copyright © 2011 by ASME


The equivalent same-order system for multi-rational-order fractional differential system with Caputo derivative is studied. With the relationship between Caputo derivative and generalized fractional derivative, we can change the multi-order fractional differential system whose fractional order is rational into a much higher-dimensional fractional differential system with the same order lying in (0,1). Based on the equivalent results, the stability analysis of any multi-rational-order fractional differential system is given. Finally, several examples are provided to illustrate the results in this paper.

Copyright © 2011 by ASME
Topics: Stability



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