Abstract
In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time fractional equations in metric measure spaces.
Funding source: National Research Foundation of Korea
Award Identifier / Grant number: 2016R1E1A1A01941893
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11522106
Funding source: Japan Society for the Promotion of Science
Award Identifier / Grant number: 26
Funding source: Natural Science Foundation of Fujian Province
Award Identifier / Grant number: 2015J01003
Funding statement: The research of Panki Kim is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1E1A1A01941893). The research of Takashi Kumagai is supported by the Grant-in-Aid for Scientific Research (A) 25247007 and 17H01093, Japan. The research of Jian Wang is supported by National Natural Science Foundation of China (No. 11522106), the JSPS postdoctoral fellowship (2604021), Fok Ying Tung Education Foundation (No. 151002), National Science Foundation of Fujian Province (No. 2015J01003), the Program for Probability and Statistics: Theory and Application (No. IRTL1704), and Fujian Provincial Key Laboratory of Mathematical Analysis and its Applications (FJKLMAA).
References
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Articles in the same Issue
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- Additive bases with coefficients of newforms
- A note on split extensions of bialgebras
- Petersson norm of cusp forms associated to real quadratic fields
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Articles in the same Issue
- Frontmatter
- Upper bounds for geodesic periods over rank one locally symmetric spaces
- Additive bases with coefficients of newforms
- A note on split extensions of bialgebras
- Petersson norm of cusp forms associated to real quadratic fields
- A realization theorem for sets of lengths in numerical monoids
- On the non-existence of the Mackey topology for locally quasi-convex groups
- The Davies method revisited for heat kernel upper bounds of regular Dirichlet forms on metric measure spaces
- The cup product of Brooks quasimorphisms
- Heat kernel estimates for time fractional equations
- Extreme non-Arens regularity of the group algebra
- Rational homology and homotopy of high-dimensional string links
- Global integrability for solutions to some anisotropic problem with nonstandard growth
- Hardy operators on Musielak–Orlicz spaces
- Contractibility of the stability manifold for silting-discrete algebras
- Order of the canonical vector bundle over configuration spaces of spheres
- An endpoint version of uniform Sobolev inequalities
- Space-time L2 estimates, regularity and almost global existence for elastic waves
- k-spaces and duals of non-archimedean metrizable locally convex spaces
- Path homology theory of multigraphs and quivers