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Monte Carlo fPINNs: Deep learning method for forward and inverse problems involving high dimensional fractional partial differential equations 期刊论文
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2022, 卷号: 400, 页码: 17
作者:  Guo, Ling;  Wu, Hao;  Yu, Xiaochen;  Zhou, Tao
收藏  |  浏览/下载：49/0  |  提交时间：2023/02/07
Physics -informed neural networks  Fractional Laplacian  Nonlocal operators  Uncertainty quantification  
Optimal Holder continuity and hitting probabilities for SPDEs with rough fractional noises 期刊论文
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 卷号: 512, 期号: 1, 页码: 21
作者:  Hong, Jialin;  Liu, Zhihui;  Sheng, Derui
收藏  |  浏览/下载：58/0  |  提交时间：2023/02/07
Stochastic partial differential equation  Fractional Brownian sheet  Hurst index H < 1/2  Holder exponent  Hitting probability  
A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition 期刊论文
JOURNAL OF COMPUTATIONAL PHYSICS, 2022, 卷号: 461, 页码: 17
作者:  Zhao, Yue;  Mao, Zhiping;  Guo, Ling;  Tang, Yifa;  Karniadakis, George Em
收藏  |  浏览/下载：58/0  |  提交时间：2023/02/07
Uncertainty quantification  Anomalous transport  Quasi Monte Carlo simulation  Generalized polynomial chaos  Long-time integration  Poly-fractonomials  
A fast Euler-Maruyama method for fractional stochastic differential equations 期刊论文
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2022, 页码: 19
作者:  Zhang, Jingna;  Tang, Yifa;  Huang, Jianfei
收藏  |  浏览/下载：62/0  |  提交时间：2023/02/07
Fractional stochastic differential equations  Euler-Maruyama method  Sum-of-exponentials approximation  Strong convergence  Computational efficiency  
Transport properties of mixed convective nano-material flow considering the generalized fourier law and a vertical surface: Concept of caputo-time fractional derivative 期刊论文
PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART A-JOURNAL OF POWER AND ENERGY, 2022, 页码: 11
作者:  Raza, Ali;  Khan, Sami Ullah;  Farid, Saadia;  Khan, Muhammad Ijaz;  Khan, M. Riaz;  Ul Haq, Absar;  Elsiddieg, Awatif M. A.;  Malik, M. Y.;  Alsallami, Shami A. M.
收藏  |  浏览/下载：61/0  |  提交时间：2023/02/07
Newtonian  slip  convective flow  fourier's law  fractional derivatives  
Simpson's method for fractional differential equations with a non-singular kernel applied to a chaotic tumor model 期刊论文
PHYSICA SCRIPTA, 2021, 卷号: 96, 期号: 12, 页码: 19
作者:  Arshad, Sadia;  Saleem, Iram;  Defterli, Ozlem;  Tang, Yifa;  Baleanu, Dumitru
收藏  |  浏览/下载：114/0  |  提交时间：2022/04/02
fractional operator with the non-singular kernel  numerical approximation  stability analysis  convergence analysis  tumor model  chaos  
Simpson’s method for fractional differential equations with a non-singular kernel applied to a chaotic tumor model 期刊论文
Physica Scripta, 2021, 卷号: 96, 期号: 12
作者:  Arshad,Sadia;  Saleem,Iram;  Defterli,Ozlem;  Tang,Yifa;  Baleanu,Dumitru
收藏  |  浏览/下载：118/0  |  提交时间：2022/04/02
fractional operator with the non-singular kernel  numerical approximation  stability analysis  convergence analysis  tumor model  chaos  
Numerical Schemes for Time-Space Fractional Vibration Equations 期刊论文
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2021, 卷号: 13, 期号: 4, 页码: 806-826
作者:  Zhang, Jingna;  Aleroev, Temirkhan S.;  Tang, Yifa;  Huang, Jianfei
收藏  |  浏览/下载：168/0  |  提交时间：2021/06/01
Time-space fractional vibration equations  ADI scheme  stability  convergence  
Optimal rate of convergence for two classes of schemes to stochastic differential equations driven by fractional Brownian motions 期刊论文
IMA JOURNAL OF NUMERICAL ANALYSIS, 2021, 卷号: 41, 期号: 2, 页码: 1608-1638
作者:  Hong, Jialin;  Huang, Chuying;  Wang, Xu
收藏  |  浏览/下载：128/0  |  提交时间：2021/10/26
fractional Brownian motion  strong convergence rate  Runge-Kutta method  simplified step-N Euler scheme  
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators 期刊论文
NATURE MACHINE INTELLIGENCE, 2021, 卷号: 3, 期号: 3, 页码: 218-+
作者:  Lu, Lu;  Jin, Pengzhan;  Pang, Guofei;  Zhang, Zhongqiang;  Karniadakis, George Em
收藏  |  浏览/下载：203/0  |  提交时间：2021/06/01