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Weak solutions of fractional differential equations in non cylindrical domains
Affiliation:1. Department of Mathematics and Information Sciences, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland;2. Institute of Applied Mathematics and Mechanics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland;1. Department of Mathematics, College of Science, Hohai University, Nanjing, 210098, PR China;2. Department of Mathematics, Nanjing University, Nanjing, 210093, PR China;3. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, PR China;1. Centre for Informatics and Computing, VAST, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Viet Nam;2. Thai Nguyen University of Economic and Business Administration, Thai Nguyen, Viet Nam;1. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, PR China;2. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, PR China;3. School of Science, Xi’an Polytechnic University, Xi’an, 710048, PR China;1. School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China;2. Department of Mathematics, Sichuan Normal University, Chengdu 610066, China
Abstract:We study a time fractional heat equation in a non cylindrical domain. The problem is one-dimensional. We prove existence of properly defined weak solutions by means of the Galerkin approximation.
Keywords:Time fractional Caputo derivative  Heat equation  Galerkin method
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