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On Fractional Heat Equation

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Abstract

In this paper, the long-time behavior of the Cesaro mean of the fundamental solution for fractional Heat equation corresponding to random time changes in the Brownian motion is studied. We consider both stable subordinators leading to equations with the Caputo-Djrbashian fractional derivative and more general cases corresponding to differential-convolution operators, in particular, distributed order derivatives.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska 3, Kyiv, 01024, Ukraine

    Anatoly N. Kochubei

  2. Department of Mathematics, University of Bielefeld, D-33615, Bielefeld, Germany

    Yuri Kondratiev

  3. CIMA, University of Madeira, Campus da Penteada, 9020-105, Funchal, Portugal

    José Luís da Silva

  4. Dragomanov University, Kyiv, Ukraine

    Yuri Kondratiev

Authors
  1. Anatoly N. Kochubei
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  2. Yuri Kondratiev
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  3. José Luís da Silva
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Kochubei, A.N., Kondratiev, Y. & da Silva, J.L. On Fractional Heat Equation. Fract Calc Appl Anal 24, 73–87 (2021). https://doi.org/10.1515/fca-2021-0004

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  • DOI: https://doi.org/10.1515/fca-2021-0004

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