WELL-POSEDNESS AND REGULARITY OF CAPUTO–HADAMARD TIME-FRACTIONAL DIFFUSION EQUATIONS

Zhiwei Yang (), Xiangcheng Zheng () and Hong Wang
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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

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-13

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.

Keywords: Ultraslow Diffusion; Mean Square Displacement; Caputo–Hadamard; Time-Fractional Diffusion Equation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500050

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