Journal
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
Volume 30, Issue 1, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218348X22500050
Keywords
Ultraslow Diffusion; Mean Square Displacement; Caputo-Hadamard; Time-Fractional Diffusion Equation
Funding
- ARO MURI Grant [W911NF-15-1-0562]
- National Science Foundation [DMS-2012291]
- National Natural Science Foundation of China [11971272]
- China Postdoctoral Science Foundation [2021TQ0017, 2021M700244]
- International Postdoctoral Exchange Fellowship Program (TalentIntroduction Program) [YJ20210019]
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This paper investigates the well-posedness and smoothing properties of a Caputo-Hadamard time-fractional diffusion model in multiple space dimensions, providing adequate descriptions for ultraslow diffusion processes.
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.
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