Nonlinear Dynamics

, Volume 95, Issue 1, pp 809–822 | Cite as

Numerical solution of fractional-order time-varying delayed differential systems using Lagrange interpolation

  • Hu Wang
  • Yajuan Gu
  • Yongguang YuEmail author
Original Paper


In this paper, a numerical solution of fractional-order time-varying delayed differential systems using Lagrange interpolation is investigated. Based on Lagrange interpolation method, the Adams–Bashforth–Moulton algorithm has been extended to solve fractional-order time-varying delayed differential systems. Furthermore, a detailed error analysis of this algorithm is presented. A fractional-order time-varying delayed Hopfield neural network as numerical example is given. In addition, the different parameters in the fractional-order time-varying delayed neural network are considered. Finally, some simple and direct numerical methods which are compared with Lagrange interpolation method in the fractional-order time-varying delayed neural network are discussed. The example with numerical simulation clearly illustrated that the present method is reliable.


Numerical solution Fractional-order Time-varying delayed differential systems Lagrange interpolation 


Compliance with ethical standards

Conflict of interest

We declare that there are no conflicts of interest.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Statistics and MathematicsCentral University of Finance and EconomicsBeijingChina
  2. 2.Department of MathematicsBeijing Jiaotong UniversityBeijingChina

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