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Results on the Approximate Controllability of Hilfer Type fractional Semilinear Control Systems

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Abstract

The approximate controllability of Hilfer fractional semilinear control systems is the main focus of this study. Two distinct kinds of necessary requirements have been investigated. For the first set of results, we use Schauder’s fixed point techniques, compactness of the relevant fractional operator, and concepts on fractional derivative to obtain them. Utilizing the Gronwall’s inequality in the second set, we are able to demonstrate the main points without using the corresponding fractional operator’s compactness or the fixed point method. Also provided is a case study for the validation of theoretical findings.

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Authors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, 632014, India

    V. Vijayakumar

  2. School of Mathematical and Statistical Sciences, Indian Institute of Technology, Mandi, Kamand, Himachal Pradesh, 175005, India

    Muslim Malik

  3. Department of Applied Sciences, Rajkiya Engineering College Kannauj, Kannauj, Uttar Pradesh, 209732, India

    Anurag Shukla

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Vijayakumar, V., Malik, M. & Shukla, A. Results on the Approximate Controllability of Hilfer Type fractional Semilinear Control Systems. Qual. Theory Dyn. Syst. 22, 58 (2023). https://doi.org/10.1007/s12346-023-00759-2

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