Zhang, Wen; Wu, Changxing; Ruan, Zhousheng; Qiu, Shufang A Jacobi spectral method for calculating fractional derivative based on mollification regularization. (English) Zbl 07799932 Asymptotic Anal. 136, No. 1, 61-77 (2024). MSC: 65M70 65M12 65M15 65D32 33C45 35B65 26A33 35R11 34A08 34B24 35R60 PDFBibTeX XMLCite \textit{W. Zhang} et al., Asymptotic Anal. 136, No. 1, 61--77 (2024; Zbl 07799932) Full Text: DOI
Atta, Ahmed G.; Abd-Elhameed, Waleed M.; Moatimid, Galal M.; Youssri, Youssri H. Novel spectral schemes to fractional problems with nonsmooth solutions. (English) Zbl 07784887 Math. Methods Appl. Sci. 46, No. 13, 14745-14764 (2023). MSC: 65L70 65D20 65L20 65L70 PDFBibTeX XMLCite \textit{A. G. Atta} et al., Math. Methods Appl. Sci. 46, No. 13, 14745--14764 (2023; Zbl 07784887) Full Text: DOI
Faustmann, Markus; Marcati, Carlo; Melenk, Jens Markus; Schwab, Christoph Exponential convergence of \(hp\)-FEM for the integral fractional Laplacian in polygons. (English) Zbl 07770179 SIAM J. Numer. Anal. 61, No. 6, 2601-2622 (2023). MSC: 65N30 65N12 65N15 26A33 35R11 PDFBibTeX XMLCite \textit{M. Faustmann} et al., SIAM J. Numer. Anal. 61, No. 6, 2601--2622 (2023; Zbl 07770179) Full Text: DOI arXiv
Tang, Bo; Chen, Yan-ping; Xie, Bin; Lin, Xiu-xiu A novel error analysis of spectral method for the anomalous subdiffusion problems with multi-term time-fractional derivative. (English) Zbl 07767311 Acta Math. Appl. Sin., Engl. Ser. 39, No. 4, 943-961 (2023). MSC: 41A60 PDFBibTeX XMLCite \textit{B. Tang} et al., Acta Math. Appl. Sin., Engl. Ser. 39, No. 4, 943--961 (2023; Zbl 07767311) Full Text: DOI
Zheng, Xiangcheng; Ervin, V. J.; Wang, Hong Analysis and Petrov-Galerkin numerical approximation for variable coefficient two-sided fractional diffusion, advection, reaction equations. (English) Zbl 1514.65182 J. Comput. Appl. Math. 425, Article ID 115033, 15 p. (2023). MSC: 65N30 35B65 41A10 33C45 PDFBibTeX XMLCite \textit{X. Zheng} et al., J. Comput. Appl. Math. 425, Article ID 115033, 15 p. (2023; Zbl 1514.65182) Full Text: DOI arXiv
Zhang, Juan; Song, Jiabin; Chen, Huanzhen A priori error estimates for spectral Galerkin approximations of integral state-constrained fractional optimal control problems. (English) Zbl 1524.65902 Adv. Appl. Math. Mech. 15, No. 3, 568-582 (2023). MSC: 65N35 65N15 49J20 35R11 26A33 33C45 65K10 49K20 65N30 PDFBibTeX XMLCite \textit{J. Zhang} et al., Adv. Appl. Math. Mech. 15, No. 3, 568--582 (2023; Zbl 1524.65902) Full Text: DOI
Zhou, Zhaojie; Wang, Fangyuan; Zheng, Xiangcheng Analysis and discretization for an optimal control problem of a variable-coefficient Riesz-fractional diffusion equation with pointwise control constraints. (English) Zbl 1524.35735 Acta Math. Sci., Ser. B, Engl. Ed. 43, No. 2, 640-654 (2023). MSC: 35R11 49M25 65N30 PDFBibTeX XMLCite \textit{Z. Zhou} et al., Acta Math. Sci., Ser. B, Engl. Ed. 43, No. 2, 640--654 (2023; Zbl 1524.35735) Full Text: DOI
Bogoya, Manuel; Grudsky, Sergei M.; Serra-Capizzano, Stefano; Tablino-Possio, Cristina Fine spectral estimates with applications to the optimally fast solution of large FDE linear systems. (English) Zbl 1502.15026 BIT 62, No. 4, 1417-1431 (2022). MSC: 15B99 15A18 65F10 26A33 PDFBibTeX XMLCite \textit{M. Bogoya} et al., BIT 62, No. 4, 1417--1431 (2022; Zbl 1502.15026) Full Text: DOI arXiv
Fu, Taibai; Du, Changfa; Xu, Yufeng An effective finite element method with shifted fractional powers bases for fractional boundary value problems. (English) Zbl 1496.65092 J. Sci. Comput. 92, No. 1, Paper No. 4, 15 p. (2022). MSC: 65L60 34A08 65L10 PDFBibTeX XMLCite \textit{T. Fu} et al., J. Sci. Comput. 92, No. 1, Paper No. 4, 15 p. (2022; Zbl 1496.65092) Full Text: DOI
Zhao, Yue; Mao, Zhiping; Guo, Ling; Tang, Yifa; Karniadakis, George Em A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition. (English) Zbl 07525181 J. Comput. Phys. 461, Article ID 111213, 17 p. (2022). MSC: 65M70 65C05 35R11 60H35 PDFBibTeX XMLCite \textit{Y. Zhao} et al., J. Comput. Phys. 461, Article ID 111213, 17 p. (2022; Zbl 07525181) Full Text: DOI
Meng, Xuhui; Yang, Liu; Mao, Zhiping; del Águila Ferrandis, José; Karniadakis, George Em Learning functional priors and posteriors from data and physics. (English) Zbl 1515.62046 J. Comput. Phys. 457, Article ID 111073, 22 p. (2022). MSC: 62F15 68T07 PDFBibTeX XMLCite \textit{X. Meng} et al., J. Comput. Phys. 457, Article ID 111073, 22 p. (2022; Zbl 1515.62046) Full Text: DOI arXiv
Colbrook, Matthew J.; Ayton, Lorna J. A contour method for time-fractional PDEs and an application to fractional viscoelastic beam equations. (English) Zbl 07518066 J. Comput. Phys. 454, Article ID 110995, 24 p. (2022). MSC: 65Mxx 65Rxx 65Lxx PDFBibTeX XMLCite \textit{M. J. Colbrook} and \textit{L. J. Ayton}, J. Comput. Phys. 454, Article ID 110995, 24 p. (2022; Zbl 07518066) Full Text: DOI arXiv
Zhang, Hui; Liu, Fawang; Jiang, Xiaoyun; Turner, Ian Spectral method for the two-dimensional time distributed-order diffusion-wave equation on a semi-infinite domain. (English) Zbl 1500.65087 J. Comput. Appl. Math. 399, Article ID 113712, 15 p. (2022). MSC: 65M70 65M60 65M06 65N35 65N30 65M12 65D32 35L05 86A05 26A33 35R11 PDFBibTeX XMLCite \textit{H. Zhang} et al., J. Comput. Appl. Math. 399, Article ID 113712, 15 p. (2022; Zbl 1500.65087) Full Text: DOI
Wang, Huasheng; Chen, Yanping; Huang, Yunqing; Mao, Wenting A Petrov-Galerkin spectral method for fractional convection-diffusion equations with two-sided fractional derivative. (English) Zbl 1480.65356 Int. J. Comput. Math. 98, No. 3, 536-551 (2021). MSC: 65N35 65N12 65N15 PDFBibTeX XMLCite \textit{H. Wang} et al., Int. J. Comput. Math. 98, No. 3, 536--551 (2021; Zbl 1480.65356) Full Text: DOI
Zhao, Lijing; Deng, Weihua; Hesthaven, Jan S. Characterization of image spaces of Riemann-Liouville fractional integral operators on Sobolev spaces \(W^{m,p} (\Omega)\). (English) Zbl 07445145 Sci. China, Math. 64, No. 12, 2611-2636 (2021). MSC: 47-XX 46-XX 26A33 46E30 34A08 34A45 65-XX PDFBibTeX XMLCite \textit{L. Zhao} et al., Sci. China, Math. 64, No. 12, 2611--2636 (2021; Zbl 07445145) Full Text: DOI arXiv
Mazza, Mariarosa B-spline collocation discretizations of Caputo and Riemann-Liouville derivatives: a matrix comparison. (English) Zbl 1498.65172 Fract. Calc. Appl. Anal. 24, No. 6, 1670-1698 (2021). MSC: 65M70 35R11 65D07 65F08 PDFBibTeX XMLCite \textit{M. Mazza}, Fract. Calc. Appl. Anal. 24, No. 6, 1670--1698 (2021; Zbl 1498.65172) Full Text: DOI
Li, Yulong On the decomposition of solutions: from fractional diffusion to fractional Laplacian. (English) Zbl 1498.35585 Fract. Calc. Appl. Anal. 24, No. 5, 1571-1600 (2021). MSC: 35R11 65L60 34A08 26A33 PDFBibTeX XMLCite \textit{Y. Li}, Fract. Calc. Appl. Anal. 24, No. 5, 1571--1600 (2021; Zbl 1498.35585) Full Text: DOI
She, Mianfu; Li, Lili; Tang, Renxuan; Li, Dongfang A novel numerical scheme for a time fractional Black-Scholes equation. (English) Zbl 1479.91446 J. Appl. Math. Comput. 66, No. 1-2, 853-870 (2021). MSC: 91G60 65M60 65M70 91G20 PDFBibTeX XMLCite \textit{M. She} et al., J. Appl. Math. Comput. 66, No. 1--2, 853--870 (2021; Zbl 1479.91446) Full Text: DOI
Fu, Taibai; Duan, Beiping; Zheng, Zhoushun An effective finite element method with singularity reconstruction for fractional convection-diffusion equation. (English) Zbl 1493.65200 J. Sci. Comput. 88, No. 3, Paper No. 59, 18 p. (2021). MSC: 65N30 65N12 65N15 35B65 35A15 35A01 35A02 26A33 35R11 PDFBibTeX XMLCite \textit{T. Fu} et al., J. Sci. Comput. 88, No. 3, Paper No. 59, 18 p. (2021; Zbl 1493.65200) Full Text: DOI
Khosravian-Arab, Hassan; Eslahchi, Mohammad Reza Müntz Sturm-Liouville problems: theory and numerical experiments. (English) Zbl 1498.34033 Fract. Calc. Appl. Anal. 24, No. 3, 775-817 (2021). MSC: 34A08 35R11 26A33 65M70 65L60 PDFBibTeX XMLCite \textit{H. Khosravian-Arab} and \textit{M. R. Eslahchi}, Fract. Calc. Appl. Anal. 24, No. 3, 775--817 (2021; Zbl 1498.34033) Full Text: DOI arXiv
Zhao, Zhengang; Zheng, Yunying Numerical approximation for fractional neutron transport equation. (English) Zbl 1477.82019 J. Math. 2021, Article ID 6676640, 14 p. (2021). MSC: 82M10 65M12 82D75 35R11 PDFBibTeX XMLCite \textit{Z. Zhao} and \textit{Y. Zheng}, J. Math. 2021, Article ID 6676640, 14 p. (2021; Zbl 1477.82019) Full Text: DOI
Mao, Wenting; Wang, Huasheng; Chen, Chuanjun A-posteriori error estimations based on postprocessing technique for two-sided fractional differential equations. (English) Zbl 1467.65072 Appl. Numer. Math. 167, 73-91 (2021). MSC: 65L10 34A08 65L60 65L70 PDFBibTeX XMLCite \textit{W. Mao} et al., Appl. Numer. Math. 167, 73--91 (2021; Zbl 1467.65072) Full Text: DOI
Zheng, Xiangcheng; Ervin, V. J.; Wang, Hong Optimal Petrov-Galerkin spectral approximation method for the fractional diffusion, advection, reaction equation on a bounded interval. (English) Zbl 1465.65154 J. Sci. Comput. 86, No. 3, Paper No. 29, 22 p. (2021). MSC: 65N30 65N35 65N12 35B65 41A10 33C45 35R11 PDFBibTeX XMLCite \textit{X. Zheng} et al., J. Sci. Comput. 86, No. 3, Paper No. 29, 22 p. (2021; Zbl 1465.65154) Full Text: DOI arXiv
Hao, Zhaopeng; Zhang, Zhongqiang Fast spectral Petrov-Galerkin method for fractional elliptic equations. (English) Zbl 1458.65155 Appl. Numer. Math. 162, 318-330 (2021). MSC: 65N35 65N30 65N12 35B65 35A01 35A02 35R11 PDFBibTeX XMLCite \textit{Z. Hao} and \textit{Z. Zhang}, Appl. Numer. Math. 162, 318--330 (2021; Zbl 1458.65155) Full Text: DOI
Ervin, V. J. Regularity of the solution to fractional diffusion, advection, reaction equations in weighted Sobolev spaces. (English) Zbl 1456.35212 J. Differ. Equations 278, 294-325 (2021). MSC: 35R11 35B65 46E35 00A20 00A22 65A05 41A55 PDFBibTeX XMLCite \textit{V. J. Ervin}, J. Differ. Equations 278, 294--325 (2021; Zbl 1456.35212) Full Text: DOI arXiv
Khosravian-Arab, Hassan; Eslahchi, M. R. Müntz pseudo-spectral method: theory and numerical experiments. (English) Zbl 1453.65358 Commun. Nonlinear Sci. Numer. Simul. 93, Article ID 105510, 29 p. (2021). MSC: 65M70 26A33 33C45 58C40 65M15 35R11 34A08 PDFBibTeX XMLCite \textit{H. Khosravian-Arab} and \textit{M. R. Eslahchi}, Commun. Nonlinear Sci. Numer. Simul. 93, Article ID 105510, 29 p. (2021; Zbl 1453.65358) Full Text: DOI arXiv
D’Elia, Marta; Du, Qiang; Glusa, Christian; Gunzburger, Max; Tian, Xiaochuan; Zhou, Zhi Numerical methods for nonlocal and fractional models. (English) Zbl 07674560 Acta Numerica 29, 1-124 (2020). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{M. D'Elia} et al., Acta Numerica 29, 1--124 (2020; Zbl 07674560) Full Text: DOI arXiv
Zhao, Jingjun; Zhang, Yanming; Xu, Yang Implicit Runge-Kutta and spectral Galerkin methods for the two-dimensional nonlinear Riesz space fractional diffusion equation. (English) Zbl 1497.65197 Appl. Math. Comput. 386, Article ID 125505, 14 p. (2020). MSC: 65M70 65L06 PDFBibTeX XMLCite \textit{J. Zhao} et al., Appl. Math. Comput. 386, Article ID 125505, 14 p. (2020; Zbl 1497.65197) Full Text: DOI
Zhang, Hui; Jiang, Xiaoyun; Zeng, Fanhai; Karniadakis, George Em A stabilized semi-implicit Fourier spectral method for nonlinear space-fractional reaction-diffusion equations. (English) Zbl 1453.65370 J. Comput. Phys. 405, Article ID 109141, 17 p. (2020). MSC: 65M70 65M15 35R11 65M12 PDFBibTeX XMLCite \textit{H. Zhang} et al., J. Comput. Phys. 405, Article ID 109141, 17 p. (2020; Zbl 1453.65370) Full Text: DOI arXiv
Lischke, Anna; Pang, Guofei; Gulian, Mamikon; Song, Fangying; Glusa, Christian; Zheng, Xiaoning; Mao, Zhiping; Cai, Wei; Meerschaert, Mark M.; Ainsworth, Mark; Karniadakis, George Em What is the fractional Laplacian? A comparative review with new results. (English) Zbl 1453.35179 J. Comput. Phys. 404, Article ID 109009, 62 p. (2020). MSC: 35R11 60G51 35A01 35A02 65N30 65C05 35-02 65-02 PDFBibTeX XMLCite \textit{A. Lischke} et al., J. Comput. Phys. 404, Article ID 109009, 62 p. (2020; Zbl 1453.35179) Full Text: DOI Link
Zheng, Xiangcheng; Ervin, Vincent J.; Wang, Hong Numerical approximations for the variable coefficient fractional diffusion equations with non-smooth data. (English) Zbl 1451.65209 Comput. Methods Appl. Math. 20, No. 3, 573-589 (2020). MSC: 65N30 35B65 41A10 33C45 PDFBibTeX XMLCite \textit{X. Zheng} et al., Comput. Methods Appl. Math. 20, No. 3, 573--589 (2020; Zbl 1451.65209) Full Text: DOI arXiv
Castillo, Paul.; Gómez, Sergio Alejandro On the convergence of the local discontinuous Galerkin method applied to a stationary one dimensional fractional diffusion problem. (English) Zbl 1452.65325 J. Sci. Comput. 85, No. 2, Paper No. 32, 21 p. (2020). MSC: 65N30 65M60 65N12 65N15 35R11 26A33 PDFBibTeX XMLCite \textit{Paul. Castillo} and \textit{S. A. Gómez}, J. Sci. Comput. 85, No. 2, Paper No. 32, 21 p. (2020; Zbl 1452.65325) Full Text: DOI
Jiang, Tao; Wang, Xing-Chi; Huang, Jin-Jing; Ren, Jin-Lian An effective pure meshfree method for 1D/2D time fractional convection-diffusion problems on irregular geometry. (English) Zbl 1464.65145 Eng. Anal. Bound. Elem. 118, 265-276 (2020). MSC: 65M70 35R11 PDFBibTeX XMLCite \textit{T. Jiang} et al., Eng. Anal. Bound. Elem. 118, 265--276 (2020; Zbl 1464.65145) Full Text: DOI
Li, Xianjuan; Mao, Zhiping; Wang, Nan; Song, Fangying; Wang, Hong; Karniadakis, George Em A fast solver for spectral elements applied to fractional differential equations using hierarchical matrix approximation. (English) Zbl 1442.65144 Comput. Methods Appl. Mech. Eng. 366, Article ID 113053, 24 p. (2020). MSC: 65L60 34A08 PDFBibTeX XMLCite \textit{X. Li} et al., Comput. Methods Appl. Mech. Eng. 366, Article ID 113053, 24 p. (2020; Zbl 1442.65144) Full Text: DOI arXiv
Minden, Victor; Ying, Lexing A simple solver for the fractional Laplacian in multiple dimensions. (English) Zbl 1437.65242 SIAM J. Sci. Comput. 42, No. 2, A878-A900 (2020). MSC: 65R20 35R11 65N06 26A33 PDFBibTeX XMLCite \textit{V. Minden} and \textit{L. Ying}, SIAM J. Sci. Comput. 42, No. 2, A878--A900 (2020; Zbl 1437.65242) Full Text: DOI arXiv
Zheng, Xiangcheng; Ervin, V. J.; Wang, Hong Wellposedness of the two-sided variable coefficient Caputo flux fractional diffusion equation and error estimate of its spectral approximation. (English) Zbl 1477.65127 Appl. Numer. Math. 153, 234-247 (2020). MSC: 65L60 34A08 PDFBibTeX XMLCite \textit{X. Zheng} et al., Appl. Numer. Math. 153, 234--247 (2020; Zbl 1477.65127) Full Text: DOI arXiv
Abbaszadeh, Mostafa; Dehghan, Mehdi; Zhou, Yong Crank-Nicolson/Galerkin spectral method for solving two-dimensional time-space distributed-order weakly singular integro-partial differential equation. (English) Zbl 1435.65170 J. Comput. Appl. Math. 374, Article ID 112739, 16 p. (2020). MSC: 65M70 65M60 65M06 65M12 65M15 35R09 45K05 33C45 26A33 35R11 PDFBibTeX XMLCite \textit{M. Abbaszadeh} et al., J. Comput. Appl. Math. 374, Article ID 112739, 16 p. (2020; Zbl 1435.65170) Full Text: DOI
Eslahchi, M. R.; Esmaili, Sakine The convergence and stability analysis of a numerical method for solving a mathematical model of language competition. (English) Zbl 1441.35237 Appl. Numer. Math. 151, 119-140 (2020). MSC: 35Q91 65M70 91F20 91-10 PDFBibTeX XMLCite \textit{M. R. Eslahchi} and \textit{S. Esmaili}, Appl. Numer. Math. 151, 119--140 (2020; Zbl 1441.35237) Full Text: DOI
Hao, Zhaopeng; Lin, Guang; Zhang, Zhongqiang Error estimates of a spectral Petrov-Galerkin method for two-sided fractional reaction-diffusion equations. (English) Zbl 1433.65211 Appl. Math. Comput. 374, Article ID 125045, 13 p. (2020). MSC: 65M60 35R11 35K57 PDFBibTeX XMLCite \textit{Z. Hao} et al., Appl. Math. Comput. 374, Article ID 125045, 13 p. (2020; Zbl 1433.65211) Full Text: DOI
Zheng, Xiangcheng; Ervin, V. J.; Wang, Hong An indirect finite element method for variable-coefficient space-fractional diffusion equations and its optimal-order error estimates. (English) Zbl 1449.65331 Commun. Appl. Math. Comput. 2, No. 1, 147-162 (2020). MSC: 65N30 35B65 41A10 33C45 35R11 26A33 65N12 35R05 PDFBibTeX XMLCite \textit{X. Zheng} et al., Commun. Appl. Math. Comput. 2, No. 1, 147--162 (2020; Zbl 1449.65331) Full Text: DOI
Hou, Dianming; Azaïez, Mejdi; Xu, Chuanju Müntz spectral method for two-dimensional space-fractional convection-diffusion equation. (English) Zbl 1518.65117 Commun. Comput. Phys. 26, No. 5, 1415-1443 (2019). MSC: 65M70 65M06 65N35 33C45 26A33 35R11 65D18 68U05 68U07 PDFBibTeX XMLCite \textit{D. Hou} et al., Commun. Comput. Phys. 26, No. 5, 1415--1443 (2019; Zbl 1518.65117) Full Text: DOI
Jia, Jinhong; Wang, Hong A fast finite volume method for conservative space-time fractional diffusion equations discretized on space-time locally refined meshes. (English) Zbl 1442.65197 Comput. Math. Appl. 78, No. 5, 1345-1356 (2019). MSC: 65M08 35R11 PDFBibTeX XMLCite \textit{J. Jia} and \textit{H. Wang}, Comput. Math. Appl. 78, No. 5, 1345--1356 (2019; Zbl 1442.65197) Full Text: DOI
Zhao, Tinggang; Mao, Zhiping; Karniadakis, George Em Multi-domain spectral collocation method for variable-order nonlinear fractional differential equations. (English) Zbl 1440.65258 Comput. Methods Appl. Mech. Eng. 348, 377-395 (2019). MSC: 65N35 34A08 65M70 PDFBibTeX XMLCite \textit{T. Zhao} et al., Comput. Methods Appl. Mech. Eng. 348, 377--395 (2019; Zbl 1440.65258) Full Text: DOI arXiv
Zhang, Qifeng; Li, Tingyue Asymptotic stability of compact and linear \(\theta \)-methods for space fractional delay generalized diffusion equation. (English) Zbl 1433.65172 J. Sci. Comput. 81, No. 3, 2413-2446 (2019). MSC: 65M06 65M15 65M12 35B40 35R11 PDFBibTeX XMLCite \textit{Q. Zhang} and \textit{T. Li}, J. Sci. Comput. 81, No. 3, 2413--2446 (2019; Zbl 1433.65172) Full Text: DOI
Wang, Haiyong Analysis of spectral approximations using eigenfunctions of fractional Sturm-Liouville problems. (English) Zbl 1442.34135 J. Sci. Comput. 81, No. 3, 1655-1677 (2019). MSC: 34L10 34L20 34A08 34B24 26A33 41A25 65L15 PDFBibTeX XMLCite \textit{H. Wang}, J. Sci. Comput. 81, No. 3, 1655--1677 (2019; Zbl 1442.34135) Full Text: DOI
Zheng, Xiangcheng; Ervin, V. J.; Wang, Hong Spectral approximation of a variable coefficient fractional diffusion equation in one space dimension. (English) Zbl 1429.65289 Appl. Math. Comput. 361, 98-111 (2019). MSC: 65N35 33C45 35R11 35B65 PDFBibTeX XMLCite \textit{X. Zheng} et al., Appl. Math. Comput. 361, 98--111 (2019; Zbl 1429.65289) Full Text: DOI arXiv
Zhang, Hui; Jiang, Xiaoyun Unconditionally convergent numerical method for the two-dimensional nonlinear time fractional diffusion-wave equation. (English) Zbl 1507.65198 Appl. Numer. Math. 146, 1-12 (2019). MSC: 65M70 65M06 65N35 65M15 42C10 PDFBibTeX XMLCite \textit{H. Zhang} and \textit{X. Jiang}, Appl. Numer. Math. 146, 1--12 (2019; Zbl 1507.65198) Full Text: DOI
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
Deng, Beichuan; Zhang, Jiwei; Zhang, Zhimin Superconvergence points of integer and fractional derivatives of special Hermite interpolations and its applications in solving FDEs. (English) Zbl 1426.65188 ESAIM, Math. Model. Numer. Anal. 53, No. 3, 1061-1082 (2019). Reviewer: Marius Ghergu (Dublin) MSC: 65N35 65M15 26A33 41A05 41A10 34B24 65L60 35R11 65N15 PDFBibTeX XMLCite \textit{B. Deng} et al., ESAIM, Math. Model. Numer. Anal. 53, No. 3, 1061--1082 (2019; Zbl 1426.65188) Full Text: DOI arXiv
Kelly, James F.; Sankaranarayanan, Harish; Meerschaert, Mark M. Boundary conditions for two-sided fractional diffusion. (English) Zbl 1416.35296 J. Comput. Phys. 376, 1089-1107 (2019). MSC: 35R11 65M12 35B30 PDFBibTeX XMLCite \textit{J. F. Kelly} et al., J. Comput. Phys. 376, 1089--1107 (2019; Zbl 1416.35296) Full Text: DOI
Cai, Min; Li, Changpin Regularity of the solution to Riesz-type fractional differential equation. (English) Zbl 1431.34008 Integral Transforms Spec. Funct. 30, No. 9, 711-742 (2019). Reviewer: Krishnan Balachandran (Coimbatore) MSC: 34A08 34A12 PDFBibTeX XMLCite \textit{M. Cai} and \textit{C. Li}, Integral Transforms Spec. Funct. 30, No. 9, 711--742 (2019; Zbl 1431.34008) Full Text: DOI
Zhang, Lu; Zhou, Zhaojie Spectral Galerkin approximation of optimal control problem governed by Riesz fractional differential equation. (English) Zbl 1425.49018 Appl. Numer. Math. 143, 247-262 (2019). MSC: 49M25 PDFBibTeX XMLCite \textit{L. Zhang} and \textit{Z. Zhou}, Appl. Numer. Math. 143, 247--262 (2019; Zbl 1425.49018) Full Text: DOI
Liu, Fang; Liang, Zongqi; Yan, Yubin Optimal convergence rates for semidiscrete finite element approximations of linear space-fractional partial differential equations under minimal regularity assumptions. (English) Zbl 1410.65348 J. Comput. Appl. Math. 352, 409-425 (2019). MSC: 65M12 65M06 65M70 35S10 PDFBibTeX XMLCite \textit{F. Liu} et al., J. Comput. Appl. Math. 352, 409--425 (2019; Zbl 1410.65348) Full Text: DOI Link
Zhang, Hui; Liu, Fawang; Jiang, Xiaoyun; Zeng, Fanhai; Turner, Ian A Crank-Nicolson ADI Galerkin-Legendre spectral method for the two-dimensional Riesz space distributed-order advection-diffusion equation. (English) Zbl 1442.65301 Comput. Math. Appl. 76, No. 10, 2460-2476 (2018). MSC: 65M70 65M12 35R09 35R11 PDFBibTeX XMLCite \textit{H. Zhang} et al., Comput. Math. Appl. 76, No. 10, 2460--2476 (2018; Zbl 1442.65301) Full Text: DOI
Chen, Sheng; Shen, Jie Enriched spectral methods and applications to problems with weakly singular solutions. (English) Zbl 1406.65123 J. Sci. Comput. 77, No. 3, 1468-1489 (2018). MSC: 65N35 65N15 65N30 35J75 PDFBibTeX XMLCite \textit{S. Chen} and \textit{J. Shen}, J. Sci. Comput. 77, No. 3, 1468--1489 (2018; Zbl 1406.65123) Full Text: DOI