Liu, Yanqin; Yin, Xiuling; Liu, Fawang; Xin, Xiaoyi; Shen, Yanfeng; Feng, Libo An alternating direction implicit Legendre spectral method for simulating a 2D multi-term time-fractional Oldroyd-B fluid type diffusion equation. (English) Zbl 1504.65224 Comput. Math. Appl. 113, 160-173 (2022). MSC: 65M70 35Q35 76A10 PDFBibTeX XMLCite \textit{Y. Liu} et al., Comput. Math. Appl. 113, 160--173 (2022; Zbl 1504.65224) Full Text: DOI
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
Zhang, Minling; Liu, Fawang; Anh, Vo An effective algorithm for computing fractional derivatives and application to fractional differential equations. (English) Zbl 1499.65073 Int. J. Numer. Anal. Model. 18, No. 4, 458-480 (2021). MSC: 65D25 26A33 34A08 65R20 PDFBibTeX XMLCite \textit{M. Zhang} et al., Int. J. Numer. Anal. Model. 18, No. 4, 458--480 (2021; Zbl 1499.65073) Full Text: Link
Liu, Qingxia; Zhuang, Pinghui; Liu, Fawang; Zheng, Minling; Chen, Shanzhen Radial point interpolation collocation method based approximation for 2D fractional equation models. (English) Zbl 1524.65667 Comput. Math. Appl. 97, 153-161 (2021). MSC: 65M70 35R11 65M06 65M12 74S40 26A33 65M15 33C45 PDFBibTeX XMLCite \textit{Q. Liu} et al., Comput. Math. Appl. 97, 153--161 (2021; Zbl 1524.65667) Full Text: DOI
Zhang, Hui; Jiang, Xiaoyun; Liu, Fawang Error analysis of nonlinear time fractional mobile/immobile advection-diffusion equation with weakly singular solutions. (English) Zbl 1488.65314 Fract. Calc. Appl. Anal. 24, No. 1, 202-224 (2021). MSC: 65M06 26A33 65M12 65M15 65M70 35R11 PDFBibTeX XMLCite \textit{H. Zhang} et al., Fract. Calc. Appl. Anal. 24, No. 1, 202--224 (2021; Zbl 1488.65314) Full Text: DOI
Wang, Ying; Liu, Fawang; Mei, Liquan; Anh, Vo V. A novel alternating-direction implicit spectral Galerkin method for a multi-term time-space fractional diffusion equation in three dimensions. (English) Zbl 1471.65166 Numer. Algorithms 86, No. 4, 1443-1474 (2021). MSC: 65M70 65M60 65M06 65M12 65M15 42C10 35Q60 35R11 PDFBibTeX XMLCite \textit{Y. Wang} et al., Numer. Algorithms 86, No. 4, 1443--1474 (2021; Zbl 1471.65166) Full Text: DOI
Zheng, Rumeng; Liu, Fawang; Jiang, Xiaoyun; Turner, Ian W. Finite difference/spectral methods for the two-dimensional distributed-order time-fractional cable equation. (English) Zbl 1452.65285 Comput. Math. Appl. 80, No. 6, 1523-1537 (2020). MSC: 65M70 35R11 65M12 65M06 65N35 42C10 PDFBibTeX XMLCite \textit{R. Zheng} et al., Comput. Math. Appl. 80, No. 6, 1523--1537 (2020; Zbl 1452.65285) Full Text: DOI
Zheng, Rumeng; Liu, Fawang; Jiang, Xiaoyun A Legendre spectral method on graded meshes for the two-dimensional multi-term time-fractional diffusion equation with non-smooth solutions. (English) Zbl 1437.65154 Appl. Math. Lett. 104, Article ID 106247, 8 p. (2020). MSC: 65M70 65M06 65M12 26A33 35R11 PDFBibTeX XMLCite \textit{R. Zheng} et al., Appl. Math. Lett. 104, Article ID 106247, 8 p. (2020; Zbl 1437.65154) Full Text: DOI
Zheng, Minling; Liu, Fawang; Jin, Zhengmeng The global analysis on the spectral collocation method for time fractional Schrödinger equation. (English) Zbl 1433.65248 Appl. Math. Comput. 365, Article ID 124689, 15 p. (2020). MSC: 65M70 35R11 81Q65 PDFBibTeX XMLCite \textit{M. Zheng} et al., Appl. Math. Comput. 365, Article ID 124689, 15 p. (2020; Zbl 1433.65248) Full Text: DOI
Zhang, Jinghua; Liu, Fawang; Lin, Zeng; Anh, Vo Analytical and numerical solutions of a multi-term time-fractional Burgers’ fluid model. (English) Zbl 1428.76148 Appl. Math. Comput. 356, 1-12 (2019). MSC: 76M22 65M70 76A10 PDFBibTeX XMLCite \textit{J. Zhang} et al., Appl. Math. Comput. 356, 1--12 (2019; Zbl 1428.76148) Full Text: DOI
Liu, Zeting; Liu, Fawang; Zeng, Fanhai An alternating direction implicit spectral method for solving two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations. (English) Zbl 1407.65114 Appl. Numer. Math. 136, 139-151 (2019). MSC: 65M06 65N35 35R11 65M12 65M15 35Q35 76A10 PDFBibTeX XMLCite \textit{Z. Liu} et al., Appl. Numer. Math. 136, 139--151 (2019; Zbl 1407.65114) Full Text: DOI arXiv
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
Liu, Zeting; Lü, Shujuan; Liu, Fawang Fully discrete spectral methods for solving time fractional nonlinear sine-Gordon equation with smooth and non-smooth solutions. (English) Zbl 1427.65292 Appl. Math. Comput. 333, 213-224 (2018). MSC: 65M70 65M12 35R11 PDFBibTeX XMLCite \textit{Z. Liu} et al., Appl. Math. Comput. 333, 213--224 (2018; Zbl 1427.65292) Full Text: DOI
Zheng, Minling; Liu, Fawang; Liu, Qingxia; Burrage, Kevin; Simpson, Matthew J. Numerical solution of the time fractional reaction-diffusion equation with a moving boundary. (English) Zbl 1415.65205 J. Comput. Phys. 338, 493-510 (2017). MSC: 65M06 65M70 35R11 35R09 65M12 65M15 PDFBibTeX XMLCite \textit{M. Zheng} et al., J. Comput. Phys. 338, 493--510 (2017; Zbl 1415.65205) Full Text: DOI
Yuan, Z. B.; Nie, Y. F.; Liu, F.; Turner, I.; Zhang, G. Y.; Gu, Y. T. An advanced numerical modeling for Riesz space fractional advection-dispersion equations by a meshfree approach. (English) Zbl 1471.65167 Appl. Math. Modelling 40, No. 17-18, 7816-7829 (2016). MSC: 65M70 35R11 PDFBibTeX XMLCite \textit{Z. B. Yuan} et al., Appl. Math. Modelling 40, No. 17--18, 7816--7829 (2016; Zbl 1471.65167) Full Text: DOI
Zheng, M.; Liu, F.; Anh, V.; Turner, I. A high-order spectral method for the multi-term time-fractional diffusion equations. (English) Zbl 1459.65205 Appl. Math. Modelling 40, No. 7-8, 4970-4985 (2016). MSC: 65M70 65M12 35R11 PDFBibTeX XMLCite \textit{M. Zheng} et al., Appl. Math. Modelling 40, No. 7--8, 4970--4985 (2016; Zbl 1459.65205) Full Text: DOI
Zheng, Minling; Liu, Fawang; Turner, Ian; Anh, Vo A novel high order space-time spectral method for the time fractional Fokker-Planck equation. (English) Zbl 1320.82052 SIAM J. Sci. Comput. 37, No. 2, A701-A724 (2015). MSC: 82C31 26A33 65M06 65N12 65M70 35R11 35Q84 PDFBibTeX XMLCite \textit{M. Zheng} et al., SIAM J. Sci. Comput. 37, No. 2, A701--A724 (2015; Zbl 1320.82052) Full Text: DOI Link
Liu, Q.; Liu, F.; Turner, I.; Anh, V.; Gu, Y. T. A RBF meshless approach for modeling a fractal mobile/immobile transport model. (English) Zbl 1354.65204 Appl. Math. Comput. 226, 336-347 (2014). MSC: 65M70 65M06 65M12 PDFBibTeX XMLCite \textit{Q. Liu} et al., Appl. Math. Comput. 226, 336--347 (2014; Zbl 1354.65204) Full Text: DOI
Zeng, Fanhai; Liu, Fawang; Li, Changpin; Burrage, Kevin; Turner, Ian; Anh, V. A Crank-Nicolson ADI spectral method for a two-dimensional Riesz space fractional nonlinear reaction-diffusion equation. (English) Zbl 1382.65349 SIAM J. Numer. Anal. 52, No. 6, 2599-2622 (2014). MSC: 65M70 35R11 65M12 65M15 35K57 PDFBibTeX XMLCite \textit{F. Zeng} et al., SIAM J. Numer. Anal. 52, No. 6, 2599--2622 (2014; Zbl 1382.65349) Full Text: DOI Link
Gu, Y. T.; Zhuang, P.; Liu, F. An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation. (English) Zbl 1231.65178 CMES, Comput. Model. Eng. Sci. 56, No. 3, 303-333 (2010). MSC: 65M70 45K05 PDFBibTeX XMLCite \textit{Y. T. Gu} et al., CMES, Comput. Model. Eng. Sci. 56, No. 3, 303--333 (2010; Zbl 1231.65178) Full Text: DOI
Song, Jiqian; Liu, Fawang; Zhuang, Pinghui An approximate solution for the non-linear anomalous subdiffusion equation using the Adomian decomposition method. (Chinese. English summary) Zbl 1164.65531 J. Xiamen Univ., Nat. Sci. 46, No. 4, 469-473 (2007). MSC: 65R20 26A33 45K05 45G10 65M70 35K55 PDFBibTeX XMLCite \textit{J. Song} et al., J. Xiamen Univ., Nat. Sci. 46, No. 4, 469--473 (2007; Zbl 1164.65531)
Ilic, M.; Liu, Fawang; Turner, I.; Anh, V. Numerical approximation of a fractional-in-space diffusion equation. I. (English) Zbl 1126.26009 Fract. Calc. Appl. Anal. 8, No. 3, 323-341 (2005). Reviewer: Rudolf Gorenflo (Berlin) MSC: 26A33 35S15 65N35 65N06 65M20 PDFBibTeX XMLCite \textit{M. Ilic} et al., Fract. Calc. Appl. Anal. 8, No. 3, 323--341 (2005; Zbl 1126.26009) Full Text: EuDML