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A novel study on a fractional-order heat conduction model for the human head by using the least-squares method

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Abstract

In this research article, a model of the temperature distribution in the human skull is considered by using the Caputo fractional derivative. When interfering thermometry is lacking, these models are quite useful in estimating the temporal course of temperatures. The given model is numerically solved with the application of the polynomial least-squares scheme. We study various fractional-order cases to simulate the proposed phenomena more clearly compared to the previously proposed integer-order studies. The motivation behind this study is to involve memory effects in the model by using fractional time derivatives.

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The data used in this study are mentioned/available in the manuscript.

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Author information

Authors and Affiliations

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

    Pushpendra Kumar

  2. Department of Mathematics, Ondokuz Mayis University, 55200, Atakum, Samsun, Turkey

    Vedat Suat Erturk

  3. Data Science Across Disciplines Research Group (Institute for the Future of Knowledge), Faculty of Engineering and the Built Environment, University of Johannesburg, PO Box 524, Auckland Park, 2006, South Africa

    Charis Harley

Authors
  1. Pushpendra Kumar
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  2. Vedat Suat Erturk
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  3. Charis Harley
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Contributions

PK was involved in conceptualization, investigation, software, resources, visualization and writing the original draft. VSE was responsible for conceptualization, investigation, software and writing—reviewing and editing. CH took part in conceptualization, supervision, formal analysis and writing—reviewing and editing.

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Correspondence to Pushpendra Kumar.

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Kumar, P., Erturk, V.S. & Harley, C. A novel study on a fractional-order heat conduction model for the human head by using the least-squares method. Int. J. Dynam. Control 11, 1040–1049 (2023). https://doi.org/10.1007/s40435-022-01051-y

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  • DOI: https://doi.org/10.1007/s40435-022-01051-y

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