Ma, Lei; Li, Rongxin; Zeng, Fanhai; Guo, Ling; Karniadakis, George Em Bi-orthogonal fPINN: a physics-informed neural network method for solving time-dependent stochastic fractional PDEs. (English) Zbl 07783920 Commun. Comput. Phys. 34, No. 4, 1133-1176 (2023). MSC: 65M32 68T07 68Q32 65C05 65M06 65D32 49M41 65M12 65M15 35R30 35R60 26A33 35R11 PDFBibTeX XMLCite \textit{L. Ma} et al., Commun. Comput. Phys. 34, No. 4, 1133--1176 (2023; Zbl 07783920) Full Text: DOI arXiv
Chen, Xuejuan; Mao, Zhiping; Karniadakis, George Em Efficient and accurate numerical methods using the accelerated spectral deferred correction for solving fractional differential equations. (English) Zbl 1524.65643 Numer. Math., Theory Methods Appl. 15, No. 4, 876-902 (2022). MSC: 65M70 65N35 65E05 41A05 41A10 41A25 26A33 35M11 65F10 65F08 34A08 65N50 65R20 PDFBibTeX XMLCite \textit{X. Chen} et al., Numer. Math., Theory Methods Appl. 15, No. 4, 876--902 (2022; Zbl 1524.65643) Full Text: DOI
Zhang, Hui; Zeng, Fanhai; Jiang, Xiaoyun; Karniadakis, George Em Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations. (English) Zbl 1503.65194 Fract. Calc. Appl. Anal. 25, No. 2, 453-487 (2022). MSC: 65M06 35R11 65M15 65M12 26A33 PDFBibTeX XMLCite \textit{H. Zhang} et al., Fract. Calc. Appl. Anal. 25, No. 2, 453--487 (2022; Zbl 1503.65194) Full Text: DOI arXiv
Cai, Min; Kharazmi, Ehsan; Li, Changpin; Karniadakis, George Em Fractional buffer layers: absorbing boundary conditions for wave propagation. (English) Zbl 1485.35376 Commun. Comput. Phys. 31, No. 2, 331-369 (2022). MSC: 35R11 35L05 26A33 65M70 76M22 PDFBibTeX XMLCite \textit{M. Cai} et al., Commun. Comput. Phys. 31, No. 2, 331--369 (2022; Zbl 1485.35376) Full Text: DOI arXiv
D’Elia, Marta; Gulian, Mamikon; Olson, Hayley; Karniadakis, George Em Towards a unified theory of fractional and nonlocal vector calculus. (English) Zbl 1498.26008 Fract. Calc. Appl. Anal. 24, No. 5, 1301-1355 (2021). MSC: 26A33 35R11 34A08 PDFBibTeX XMLCite \textit{M. D'Elia} et al., Fract. Calc. Appl. Anal. 24, No. 5, 1301--1355 (2021; Zbl 1498.26008) Full Text: DOI arXiv
Shin, Yeonjong; Darbon, Jérôme; Karniadakis, George Em A Caputo fractional derivative-based algorithm for optimization. arXiv:2104.02259 Preprint, arXiv:2104.02259 [math.OC] (2021). MSC: 65K05 65B99 26A33 BibTeX Cite \textit{Y. Shin} et al., ``A Caputo fractional derivative-based algorithm for optimization'', Preprint, arXiv:2104.02259 [math.OC] (2021) Full Text: arXiv OA License
Guo, Ling; Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em Efficient multistep methods for tempered fractional calculus: algorithms and simulations. (English) Zbl 07099350 SIAM J. Sci. Comput. 41, No. 4, A2510-A2535 (2019). MSC: 65-XX 26A33 65M06 65M12 65M15 35R11 PDFBibTeX XMLCite \textit{L. Guo} et al., SIAM J. Sci. Comput. 41, No. 4, A2510--A2535 (2019; Zbl 07099350) Full Text: DOI arXiv
Wang, Nan; Mao, Zhiping; Huang, Chengming; Karniadakis, George Em A spectral penalty method for two-sided fractional differential equations with general boundary conditions. (English) Zbl 1501.65143 SIAM J. Sci. Comput. 41, No. 3, A1840-A1866 (2019). MSC: 65N35 65E05 65M70 41A05 41A10 41A25 35D30 35A01 35A02 26A33 35R11 PDFBibTeX XMLCite \textit{N. Wang} et al., SIAM J. Sci. Comput. 41, No. 3, A1840--A1866 (2019; Zbl 1501.65143) Full Text: DOI arXiv
Zeng, Fanhai; Turner, Ian; Burrage, Kevin; Karniadakis, George Em A new class of semi-implicit methods with linear complexity for nonlinear fractional differential equations. (English) Zbl 1404.65105 SIAM J. Sci. Comput. 40, No. 5, A2986-A3011 (2018). MSC: 65M06 26A33 65M12 65M15 35R11 PDFBibTeX XMLCite \textit{F. Zeng} et al., SIAM J. Sci. Comput. 40, No. 5, A2986--A3011 (2018; Zbl 1404.65105) Full Text: DOI arXiv
Zeng, Fanhai; Mao, Zhiping; Karniadakis, George Em A generalized spectral collocation method with tunable accuracy for fractional differential equations with end-point singularities. (English) Zbl 1431.65193 SIAM J. Sci. Comput. 39, No. 1, A360-A383 (2017). MSC: 65M70 26A33 35R11 65M12 65M15 PDFBibTeX XMLCite \textit{F. Zeng} et al., SIAM J. Sci. Comput. 39, No. 1, A360--A383 (2017; Zbl 1431.65193) Full Text: DOI