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Well-posedness and stability of a fractional heat-conductor with fading memory

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Abstract

We consider a problem which describes the heat diffusion in a complex media with fading memory. The model involves a fractional time derivative of order between zero and one instead of the classical first order derivative. The model takes into account also the effect of a neutral delay. We discuss the existence and uniqueness of a mild solution as well as a classical solution. Then, we prove a Mittag-Leffler stability result. Unlike the integer-order case, we run into considerable difficulties when estimating some problematic terms. It is found that even without the memory term in the heat flux expression, the stability is still of Mittag-Leffler type.

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Acknowledgements

The authors acknowledge financial support from Sultan Qaboos University through internal grant no. IG/SCI/MATH/20/01. The second author is very grateful for the financial support and the facilities provided by King Fahd University of Petroleum and Minerals, Interdisciplinary Research Center for Intelligent Manufacturing & Robotics through project number Sb201014.

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Authors and Affiliations

  1. Department of Mathematics, Sultan Qaboos University, P.O. Box 36, Al-Khoudh 123, Muscat, Oman

    Sebti Kerbal

  2. IRC for Intelligent Manufacturing and Robotics, Department of Mathematics, King Fahd University of Petroleum and Minerals, 31261, Dhahran, Saudi Arabia

    Nasser-eddine Tatar

  3. Department of Applied Mathematics and Science, National University of Science and Technology, Muscat, Oman

    Nasser Al-Salti

  4. FracDiff Research Group (DR/RG/03), Sultan Qaboos University, Muscat, Oman

    Sebti Kerbal & Nasser Al-Salti

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  1. Sebti Kerbal
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  2. Nasser-eddine Tatar
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  3. Nasser Al-Salti
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Correspondence to Sebti Kerbal.

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Kerbal, S., Tatar, Ne. & Al-Salti, N. Well-posedness and stability of a fractional heat-conductor with fading memory. Fract Calc Appl Anal (2024). https://doi.org/10.1007/s13540-024-00291-3

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  • DOI: https://doi.org/10.1007/s13540-024-00291-3

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