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Some novel analyses of the Caputo-type singular three-point fractional boundary value problems

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Abstract

In this article, we consider singular three-point second-order boundary value problems in the sense of the Caputo fractional derivatives. We derive some novel results on the existence of a unique solution for the proposed problems. The problems are numerically solved using the least squares method and neural network scheme. We compare the solutions obtained from both approaches. The fractional-order generalization of the proposed problem, the existence and uniqueness approach, and the numerical solutions are the novel features of this study.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Puducherry, Karaikal, 609609, India

    R. Poovarasan, S. M. Sivalingam & V. Govindaraj

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

    Pushpendra Kumar

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  1. R. Poovarasan
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  2. Pushpendra Kumar
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  3. S. M. Sivalingam
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  4. V. Govindaraj
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All the authors equally contributed to the work.

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Correspondence to Pushpendra Kumar.

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Communicated by S. Ponnusamy.

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Poovarasan, R., Kumar, P., Sivalingam, S.M. et al. Some novel analyses of the Caputo-type singular three-point fractional boundary value problems. J Anal 32, 637–658 (2024). https://doi.org/10.1007/s41478-023-00638-8

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  • DOI: https://doi.org/10.1007/s41478-023-00638-8

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