Global well‐posedness of space‐time fractional diffusion equation with Rockland operator on graded lie group
In this article, we examine the general space‐time fractional diffusion equation for left‐invariant hypoelliptic homogeneous operators on graded Lie groups. Our study covers important examples such as the time fractional diffusion equation, the space‐time fractional diffusion equation when diffusion is under the influence of sub‐Laplacian on the Heisenberg group, or general stratified Lie groups. We establish the global well‐posedness of the Cauchy problem for the general space‐time fractional diffusion equation of the Rockland operator on a graded Lie group in the associated Sobolev spaces and also develop some regularity estimates for it.
Authors
- Michael Ruzhansky (ORCID: https://orcid.org/0000-0001-8633-5570)
- Aparajita Dasgupta (ORCID: https://orcid.org/0000-0001-7093-8158)
- Abhilash Tushir (ORCID: https://orcid.org/0009-0001-2870-0979)
Institutions
- Queen Mary University of London (GB)
- Ghent University (BE)
- Indian Institute of Technology Delhi (IN)
Publication Details
- Journal
- Mathematical Methods in the Applied Sciences
- Published
- 2024-11-11
- DOI
- https://doi.org/10.1002/mma.10583
- Primary Topic
- Fractional Differential Equations Solutions
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Department of Science and Technology, Ministry of Science and Technology, India
- Fonds Wetenschappelijk Onderzoek
- Universiteit Gent
- Indian Institute of Technology Delhi
- Engineering and Physical Sciences Research Council
- Science and Engineering Research Board
- Bijzonder Onderzoeksfonds UGent