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An application of fixed point technique of Rothe’s-type to interpret the controllability criteria of neutral nonlinear fractional ordered impulsive system

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  • Lakshmi Priya, P.K.
  • Kaliraj, K.

Abstract

The novel findings of this research utilizes Rothe’s fixed point technique to examine the relative controllability of neutral impulsive nonlinear differential system of arbitrary order β∈(0,1). We use pseudo-transition matrix and the technique of Laplace transform to obtain the existence results. On considering the linear form of the system to be relatively controllable as our main hypothesis, we utilize fixed point argument of Rothe’s type to establish the required conditions which are sufficiently enough for the nonlinear system to admit relative controllability. Examples are provided to validate the accuracy of the derived results and finally we apply the obtained techniques to practically model a three solution mixer.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008268
    DOI: 10.1016/j.chaos.2022.112647
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    References listed on IDEAS

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    1. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Nisar, Kottakkaran Sooppy & Shukla, Anurag, 2022. "A note concerning to approximate controllability of Atangana-Baleanu fractional neutral stochastic systems with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Nisar, Kottakkaran Sooppy & Jothimani, K. & Kaliraj, K. & Ravichandran, C., 2021. "An analysis of controllability results for nonlinear Hilfer neutral fractional derivatives with non-dense domain," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. Kaliraj, K. & Manjula, M. & Ravichandran, C., 2022. "New existence results on nonlocal neutral fractional differential equation in concepts of Caputo derivative with impulsive conditions," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    4. 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).
    5. S. Karthikeyan & K. Balachandran, 2013. "On controllability for a class of stochastic impulsive systems with delays in control," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(1), pages 67-76.
    6. Jerzy Klamka, 2020. "Controllability of Semilinear Systems with Multiple Variable Delays in Control," Mathematics, MDPI, vol. 8(11), pages 1-9, November.
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    Cited by:

    1. Wang, Xuezhen & Zhang, Huasheng, 2023. "Intelligent control of convergence rate of impulsive dynamic systems affected by nonlinear disturbances under stabilizing impulses and its application in Chua’s circuit," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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