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Well-Posedness And Regularity Of Caputo–Hadamard Time-Fractional Diffusion Equations

Author

Listed:
  • ZHIWEI YANG

    (School of Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China)

  • XIANGCHENG ZHENG

    (School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China)

  • HONG WANG

    (Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA)

Abstract

Ultraslow diffusion describes the long-time diffusion of particles whose mean square displacement (MSD) grows logarithmically in time. We prove the well-posedness of a Caputo–Hadamard time-fractional diffusion model in multiple space dimensions, in which the MSD in time grows logarithmically and thus provides adequate descriptions for the ultraslow diffusion processes, as well as the smoothing properties of the solutions.

Suggested Citation

  • Zhiwei Yang & Xiangcheng Zheng & Hong Wang, 2022. "Well-Posedness And Regularity Of Caputo–Hadamard Time-Fractional Diffusion Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-13, February.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:01:n:s0218348x22500050
    DOI: 10.1142/S0218348X22500050
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