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Existence of the solution and stability for a class of variable fractional order differential systems

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  • Jiang, Jingfei
  • Chen, Huatao
  • Guirao, Juan L.G.
  • Cao, Dengqing

Abstract

In this paper, the existence results of the solution and stability are focused for the variable fractional order differential equation. In view of the definitions of three kinds of Caputo variable fractional order operator, the sufficient condition of the solution existence for the variable fractional order differential system is obtained by use of Arzela–Ascoli theorem. Moreover, some criterions of the Mittag–Leffler stability and asymptotical stability are proposed for the variable fractional order differential system according to the Fractional Comparison Principle.

Suggested Citation

  • Jiang, Jingfei & Chen, Huatao & Guirao, Juan L.G. & Cao, Dengqing, 2019. "Existence of the solution and stability for a class of variable fractional order differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 269-274.
    • Handle: RePEc:eee:chsofr:v:128:y:2019:i:c:p:269-274
    DOI: 10.1016/j.chaos.2019.07.052
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    References listed on IDEAS

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    1. Jingfei Jiang & Dengqing Cao & Huatao Chen & Kun Zhao, 2017. "The vibration transmissibility of a single degree of freedom oscillator with nonlinear fractional order damping," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(11), pages 2379-2393, August.
    2. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
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    Cited by:

    1. Chauhan, Archana & Gautam, G.R. & Chauhan, S.P.S. & Dwivedi, Arpit, 2023. "A validation on concept of formula for variable order integral and derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Ren, Lei & Lin, Ming-Hung & Abdulwahab, Abdulkareem & Ma, Jun & Saberi-Nik, Hassan, 2023. "Global dynamical analysis of the integer and fractional 4D hyperchaotic Rabinovich system," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Duc, Tran Minh & Van Hoa, Ngo, 2021. "Stabilization of impulsive fractional-order dynamic systems involving the Caputo fractional derivative of variable-order via a linear feedback controller," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    4. Peng, Xiao & Wang, Yijing & Zuo, Zhiqiang, 2022. "Co-design of state-dependent switching law and control scheme for variable-order fractional nonlinear switched systems," Applied Mathematics and Computation, Elsevier, vol. 415(C).
    5. Zhenduo Sun & Nengneng Qing & Xiangzhi Kong, 2023. "Asymptotic Hybrid Projection Lag Synchronization of Nonidentical Variable-Order Fractional Complex Dynamic Networks," Mathematics, MDPI, vol. 11(13), pages 1-17, June.

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