文献类型：期刊文献

英文题名：A New Method for Solving the Distributed-Order Time-Fractional Mobile-Immobile Equations

作者：Du, Hong[1]; Yang, Xinyue[2]; Chen, Zhong[3]

机构：[1] College of Mathematics and Computer Science, GuangDong Ocean University, Guangdong, Zhanjiang, 524000, China; [2] College of Earth and Environmental Sciences, Lanzhou University, Gansu, Lanzhou, 730000, China; [3] Department of Mathematics, Harbin Institute of Technology at Weihai, Shandong, 264209, China

年份：2023

外文期刊名：SSRN

收录：EI(收录号：20230322187)

语种：英文

外文关键词：Multilayer neural networks

外文摘要：A new method is proposed for solving the distributed-order time-fractional mobile-immobile equation (TFM-IME) with three spatial variables. This new method compromises neural network’s huge expressive power and advantages of computations of meshless methods. It’s well known that the cost of computations is unbearable for solving high dimension space equations, even if it’s three-dimensional. To illustrate our ideas, we choose the 3D distributed-order TFM-IME, our important contribution are overcoming the difficulty of the cost of constructing 3D dense functions set and establishing approximation and convergence order theories based on neural network. Herein, a single hidden layer neural network is only applies to approximate the solution in high dimensions space using neural network’s huge expressive power. It makes the construction of dense function sets easier. And then, using the technologies of solving MRASs, the cost of calculations becomes acceptable in high dimensions space. Experiments demonstrate the effectiveness of the method. ? 2023, The Authors. All rights reserved.