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On a study for the neutral Caputo fractional multi-delayed differential equations with noncommutative coefficient matrices

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  • Aydin, Mustafa
  • Mahmudov, Nazim I.

Abstract

The representation of a solution to a neutral linear fractional multiple-delay differential inhomogeneous system with non-commutative coefficient matrices is studied using a multiple-delay perturbation of a matrix function of the Mittag-Leffler type. Second, the existence and uniqueness of the solution are discussed along with the Ulam-Hyers stability of a semilinear neutral fractional differential with multiple delays. Thirdly, with the help of the Krasnoselskii's fixed point theorem, a sufficient condition for the relative controllability of a semilinear neutral fractional differential system with multiple-delay is obtained. Numerical examples confirm the theoretical conclusions.

Suggested Citation

  • Aydin, Mustafa & Mahmudov, Nazim I., 2022. "On a study for the neutral Caputo fractional multi-delayed differential equations with noncommutative coefficient matrices," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005823
    DOI: 10.1016/j.chaos.2022.112372
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    References listed on IDEAS

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    1. Hai Zhang & Jinde Cao & Wei Jiang, 2013. "General Solution of Linear Fractional Neutral Differential Difference Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-7, June.
    2. Mahmudov, Nazim I. & Aydın, Mustafa, 2021. "Representation of solutions of nonhomogeneous conformable fractional delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Li, Mengmeng & Wang, JinRong, 2018. "Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 254-265.
    4. Elshenhab, Ahmed M. & Wang, Xing Tao, 2021. "Representation of solutions of linear differential systems with pure delay and multiple delays with linear parts given by non-permutable matrices," Applied Mathematics and Computation, Elsevier, vol. 410(C).
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