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Exact Controllability of Hilfer Fractional Differential System with Non-instantaneous Impluleses and State Dependent Delay

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Abstract

In this article, we discuss the exact controllability of a fractional order differential system involving Hilfer fractional(HF) derivative, state-dependent delay function and impulsive conditions. To obtain the proposed result, we use the semigroup theory, theory of measure of non-compactness and fixed point technique. Finally, an example is given to illustrate the application of the obtained results.

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Acknowledgements

” This study is supported via funding from Prince Sattam bin Abdulaziz University project number (PSAU/2023/R/1444). ” The authors Aziz Khan and Thabet Abdeljawad would like to thank Prince Sultan University for paying the APC and the support through TAS research lab.

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Authors and Affiliations

  1. Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh, 11586, Saudi Arabia

    Aziz Khan & Thabet Abdeljawad

  2. Department of Mathematics, Guizhou University, 550025, Guiyang, People’s Republic of China

    Qura Tul Ain

  3. Department of Medical Research, China Medical University, 40402, Taichung, Taiwan

    Thabet Abdeljawad

  4. Department of Mathematics, College of Sciences and Humanities, Prince Sattam bin Abdulaziz University, Al Kharj, Saudi Arabia

    Kottakkaran Sooppy Nisar

Authors
  1. Aziz Khan
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  2. Qura Tul Ain
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  3. Thabet Abdeljawad
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  4. Kottakkaran Sooppy Nisar
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Contributions

Conceptualization, AK, QA; Writing Original Draft: AK, QA, TA, KSN; Software: AK, KSN; Formal Analysis: TA; Validation: AK, ,TA, KSN.

Corresponding authors

Correspondence to Thabet Abdeljawad or Kottakkaran Sooppy Nisar.

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Khan, A., Ain, Q.T., Abdeljawad, T. et al. Exact Controllability of Hilfer Fractional Differential System with Non-instantaneous Impluleses and State Dependent Delay. Qual. Theory Dyn. Syst. 22, 62 (2023). https://doi.org/10.1007/s12346-023-00761-8

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  • DOI: https://doi.org/10.1007/s12346-023-00761-8

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