Variational problem containing psi-RL complex-order fractional derivatives

Jiangbo Zhao, Shuo Qin, Junzheng Wang, Shumao Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The main purpose of this paper is to solve the variational problem containing real- and complex-order fractional derivatives. We define a new version of the complex-order derivative based on the ψ-Riemann-Liouville fractional derivative, and get the Euler–Lagrange equation for the variational problem. By introducing the approximated expansion formula of the complex-order fractional derivative to the variational problem, we derive the corresponding approximated Euler–Lagrange equation. It is proved that the approximated Euler–Lagrange equation converges to the original one in the weak sense. At the same time, the minimal value of the approximated action integral tends to the minimal value of the original one. We also conduct a stress relaxation experiment and discuss the feasibility of the complex-order derivative in real problem modeling.

Original languageEnglish
Pages (from-to)1792-1802
Number of pages11
JournalAsian Journal of Control
Volume23
Issue number4
DOIs
Publication statusPublished - Jul 2021
Externally publishedYes

Keywords

  • Complex-order fractional variational problem
  • Euler–Lagrange equation
  • Expansion formula
  • Minimization problem
  • Noether's theorem
  • ψ-RL fractional derivative

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