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Controllability of nonlinear fractional Langevin systems using \({\varPsi }\)-Caputo fractional derivative

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Abstract

This paper deals with the total controllability results for nonlinear fractional Langevin systems involving \({\varPsi }\)-Caputo fractional derivatives. The controllability of a linear fractional Langevin dynamical system with \({\varPsi }\)-Caputo fractional derivatives is obtained by using the Grammian matrix. Sufficient conditions for the fractional nonlinear systems are established by using Banach’s fixed point theorem and the successive approximation method to demonstrate the total controllability of the results. Finally, an example is given to illustrate our findings.

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Authors and Affiliations

  1. Department of Mathematics, Bharathiar University, Coimbatore, 641 046, India

    D. Prabu & N. Annapoorani

  2. School of Sciences, National Institute of Technology Andhra Pradesh, Tadepalligudem, 534101, India

    P. Suresh Kumar

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  1. D. Prabu
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  2. P. Suresh Kumar
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  3. N. Annapoorani
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The authors declare that the study was realized in collaboration with equal responsibility. All authors read and approved the final manuscript.

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Correspondence to D. Prabu.

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Prabu, D., Kumar, P.S. & Annapoorani, N. Controllability of nonlinear fractional Langevin systems using \({\varPsi }\)-Caputo fractional derivative. Int. J. Dynam. Control 12, 190–199 (2024). https://doi.org/10.1007/s40435-023-01277-4

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  • DOI: https://doi.org/10.1007/s40435-023-01277-4

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