A stability analysis for multi-term fractional delay differential equations with higher order

Zhanwen Yang, Qi Li and Zichen Yao

Chaos, Solitons & Fractals, 2023, vol. 167, issue C

Abstract: As a widely used tool modeling some processes and systems in a variety of fields, fractional delay differential equations (FDDEs) with higher order have attracted much attention of the scientific community for years. Motivated by Yao et al. (2022), in which a single term has been done, we are much more interested in the stability analysis for multi-term FDDEs. In addition to the widely used Laplace transform method and decoupling technique for the characteristic equation, a region embedding technique is first introduced to handle the multiple fractional exponents. The existing results are generalized to multi-term FDDEs with higher order and the damping term of the classical integer-order delay differential equation is extended to fractional calculus. Numerical simulations for FDDEs and time-fractional telegraph equations with time delay are presented to illustrate the efficiency and validity of our results.

Keywords: Fractional delay differential equations; Caputo’s fractional derivative; Stability; Laplace transform; Region embedding technique (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:167:y:2023:i:c:s0960077922011766

DOI: 10.1016/j.chaos.2022.112997

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