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Results on the existence, uniqueness, and controllability of neutral fractional differential equations in the sense of Atangana-Baleanu derivative

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Abstract

In this manuscript, we study multi-derivative non-linear fractional neutral differential equations with non-local conditions using the Atangana-Baleanu (AB) fractional derivative. We derive some novel analyses of the existence, uniqueness and controllability of the solution. Fundamentals of the fixed-point theory are used to achieve the desired results. Finally, an illustrative example is given to verify the theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, Adithya Institute of Technology, Krumbapalayam, Coimbatore, Tamil Nadu, 641 107, India

    Palaniyappan Kalamani

  2. Department of Mathematics, Rathinam Group of Institutions, Kovilpalayam Campus, Coimbatore, Tamil Nadu, 641 107, India

    A. Stephan Antony Raj

  3. Institute for the Future of Knowledge, University of Johannesburg, PO Box 524, Auckland Park 2006, Johannesburg, South Africa

    Pushpendra Kumar

Authors
  1. Palaniyappan Kalamani
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  2. A. Stephan Antony Raj
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  3. Pushpendra Kumar
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All authors contributed equally, The final manuscript was read and approved by all authors.

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Correspondence to Pushpendra Kumar.

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Communicated by S Ponnusamy.

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Kalamani, P., Raj, A.S.A. & Kumar, P. Results on the existence, uniqueness, and controllability of neutral fractional differential equations in the sense of Atangana-Baleanu derivative. J Anal (2023). https://doi.org/10.1007/s41478-023-00685-1

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