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Forum Mathematicum

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Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


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Volume 30, Issue 5

Issues

Heat kernel estimates for time fractional equations

Zhen-Qing Chen / Panki Kim
  • Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Building 27, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea
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/ Takashi Kumagai / Jian Wang
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  • College of Mathematics and Informatics and Fujian Key Laboratory of Mathematical Analysis and Applications (FJKLMAA), Fujian Normal University, 350007 Fuzhou, P. R. China
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Published Online: 2018-02-16 | DOI: https://doi.org/10.1515/forum-2017-0192

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.

Keywords: Dirichlet form; subordinator; Caputo derivative; heat kernel estimates; time fractional equation

MSC 2010: 60G52; 60J25; 60J55; 60J35; 60J75

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About the article


Received: 2017-09-09

Published Online: 2018-02-16

Published in Print: 2018-09-01


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

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).


Citation Information: Forum Mathematicum, Volume 30, Issue 5, Pages 1163–1192, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2017-0192.

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