@article{d4c2ee44c88f45768132feca08eba949,
title = "Heat kernel estimates for time fractional equations",
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 = "Caputo derivative, Dirichlet form, heat kernel estimates, subordinator, time fractional equation",
author = "Chen, {Zhen Qing} and Panki Kim and Takashi Kumagai and Jian Wang",
note = "Funding Information: 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 (26.04021), 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). Funding Information: Funding: 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 (26⋅04021), 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). Publisher Copyright: {\textcopyright} 2018 Walter de Gruyter GmbH, Berlin/Boston.",
year = "2018",
month = sep,
day = "1",
doi = "10.1515/forum-2017-0192",
language = "English",
volume = "30",
pages = "1163--1192",
journal = "Forum Mathematicum",
issn = "0933-7741",
publisher = "Walter de Gruyter GmbH & Co. KG",
number = "5",
}