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Relative controllability analysis of fractional order differential equations with multiple time delays

Author

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  • Vadivoo, B.S.
  • Jothilakshmi, G.
  • Almalki, Y.
  • Debbouche, A.
  • Lavanya, M.

Abstract

This paper is concerned with the relative controllability for a class of fractional differential equations with multiple time delays. The solution representation is introduced for this system via multiple delayed perturbations of Mittag-Leffler function. Necessary and sufficient conditions for the indicated problem to be relatively controllable are established for linear and non-linear systems. For non-linear case, the existence result is proved by using Krasnoselskii’s fixed point theorem. Numerical examples are given to illustrate the theoretical results, and its diagrammatic formulations are done by MATLAB.

Suggested Citation

  • Vadivoo, B.S. & Jothilakshmi, G. & Almalki, Y. & Debbouche, A. & Lavanya, M., 2022. "Relative controllability analysis of fractional order differential equations with multiple time delays," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    • Handle: RePEc:eee:apmaco:v:428:y:2022:i:c:s0096300322002661
    DOI: 10.1016/j.amc.2022.127192
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    References listed on IDEAS

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    1. Kumar, Vipin & Malik, Muslim & Debbouche, Amar, 2021. "Stability and controllability analysis of fractional damped differential system with non-instantaneous impulses," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    2. Liu, Bo & Su, Housheng & Wu, Licheng & Shen, Xixi, 2021. "Controllability for multi-agent systems with matrix-weight-based signed network," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    3. Sathiyaraj, T. & Fečkan, Michal & Wang, JinRong, 2020. "Null controllability results for stochastic delay systems with delayed perturbation of matrices," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
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    Cited by:

    1. Lakshmi Priya, P.K. & Kaliraj, K., 2022. "An application of fixed point technique of Rothe’s-type to interpret the controllability criteria of neutral nonlinear fractional ordered impulsive system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Huang, Jizhao & Luo, Danfeng & Zhu, Quanxin, 2023. "Relatively exact controllability for fractional stochastic delay differential equations of order κ∈(1,2]," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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