A stability analysis for multi-term fractional delay differential equations with higher order. (February 2023) - Yang, Zhanwen; Li, Qi; Yao, Zichen
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. Highlights: A novel condition for the stability is expressed in an algebraical criterion. The Laplace transform method and a method of region embedding are used. Our results extend the stability results in Yao et al. (2022) to the multi-term FDDEs. The attenuation phenomenon of the damping term is generalized to FDDEs.