Stability criteria of arbitrary-order neutral dynamic systems with mixed delays

  • Rabha W. Ibrahim
  • Hemant K. Nashine


The stability of a neutral dynamic system is a major study in the class of delay systems. In this effort, we study the stability of fractional-order nonlinear dynamic systems utilizing Lyapunov direct method based on fractional calculus (fractional differential operator and fractional integral operator type Riemann–Liouville operators). We suggest a new non-Lipschitz fractional Lyapunov function. This function is a generalization of the well known Lyapunov functions. We investigate the speed of convergence for special cases. Applications are clarified in the sequel.


Fractional calculus Fractional differential equation Fractional differential operator stability 



The authors would like to thank the reviewers for their useful reports. The second author is thankful to the United State-India Education Foundation, New Delhi, India and IIE/CIES, Washington, DC, USA for Fulbright-Nehru PDF Award (No. 2052/FNPDR/2015).


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Computer Science and Information TechnologyUniversity of MalayaKuala LumpurMalaysia
  2. 2.Department of MathematicsTexas A & M UniversityKingsvilleUSA

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