An, Xingyu; Wang, Qingxia (Jenny); Liu, Fawang; Anh, Vo V.; Turner, Ian W. Parameter estimation for time-fractional Black-Scholes equation with S&P 500 index option. (English) Zbl 07785640 Numer. Algorithms 95, No. 1, 1-30 (2024). MSC: 91G60 65M06 91G20 PDFBibTeX XMLCite \textit{X. An} et al., Numer. Algorithms 95, No. 1, 1--30 (2024; Zbl 07785640) Full Text: DOI OA License
Feng, Libo; Liu, Fawang; Anh, Vo V. Galerkin finite element method for a two-dimensional tempered time-space fractional diffusion equation with application to a Bloch-Torrey equation retaining Larmor precession. (English) Zbl 07700836 Math. Comput. Simul. 206, 517-537 (2023). MSC: 65-XX 82-XX PDFBibTeX XMLCite \textit{L. Feng} et al., Math. Comput. Simul. 206, 517--537 (2023; Zbl 07700836) Full Text: DOI
Feng, Libo; Liu, Fawang; Anh, Vo V.; Qin, Shanlin Analytical and numerical investigation on the tempered time-fractional operator with application to the Bloch equation and the two-layered problem. (English) Zbl 1521.65073 Nonlinear Dyn. 109, No. 3, 2041-2061 (2022). MSC: 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{L. Feng} et al., Nonlinear Dyn. 109, No. 3, 2041--2061 (2022; Zbl 1521.65073) Full Text: DOI arXiv
Zhang, Mengchen; Liu, Fawang; Turner, Ian W.; Anh, Vo V. A vertex-centred finite volume method for the 3D multi-term time and space fractional Bloch-Torrey equation with fractional Laplacian. (English) Zbl 1503.65206 Commun. Nonlinear Sci. Numer. Simul. 114, Article ID 106666, 20 p. (2022). Reviewer: Abdallah Bradji (Annaba) MSC: 65M08 65M06 65N08 65M12 65M15 65F10 65F08 65F50 33E12 26A33 35R11 78A50 35Q60 PDFBibTeX XMLCite \textit{M. Zhang} et al., Commun. Nonlinear Sci. Numer. Simul. 114, Article ID 106666, 20 p. (2022; Zbl 1503.65206) Full Text: DOI
Zheng, Minling; Jin, Zhengmeng; Liu, Fawang; Anh, Vo Matrix transfer technique for anomalous diffusion equation involving fractional Laplacian. (English) Zbl 1484.65238 Appl. Numer. Math. 172, 242-258 (2022). MSC: 65M60 35R11 65M12 PDFBibTeX XMLCite \textit{M. Zheng} et al., Appl. Numer. Math. 172, 242--258 (2022; Zbl 1484.65238) 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
Lai, Junjiang; Liu, Fawang; Anh, Vo V.; Liu, Qingxia A space-time finite element method for solving linear Riesz space fractional partial differential equations. (English) Zbl 1480.65262 Numer. Algorithms 88, No. 1, 499-520 (2021). MSC: 65M60 65N30 65N12 65M15 26A33 35R11 PDFBibTeX XMLCite \textit{J. Lai} et al., Numer. Algorithms 88, No. 1, 499--520 (2021; Zbl 1480.65262) Full Text: DOI
Zhang, Mengchen; Liu, Fawang; Turner, Ian W.; Anh, Vo V.; Feng, Libo A finite volume method for the two-dimensional time and space variable-order fractional Bloch-Torrey equation with variable coefficients on irregular domains. (English) Zbl 1504.65188 Comput. Math. Appl. 98, 81-98 (2021). MSC: 65M08 35R11 65M12 PDFBibTeX XMLCite \textit{M. Zhang} et al., Comput. Math. Appl. 98, 81--98 (2021; Zbl 1504.65188) Full Text: DOI
An, Xingyu; Liu, Fawang; Zheng, Minling; Anh, Vo V.; Turner, Ian W. A space-time spectral method for time-fractional Black-Scholes equation. (English) Zbl 1466.91320 Appl. Numer. Math. 165, 152-166 (2021). MSC: 91G20 26A33 PDFBibTeX XMLCite \textit{X. An} et al., Appl. Numer. Math. 165, 152--166 (2021; Zbl 1466.91320) Full Text: DOI
Xu, Tao; Liu, Fawang; Lü, Shujuan; Anh, Vo V. Numerical approximation of 2D multi-term time and space fractional Bloch-Torrey equations involving the fractional Laplacian. (English) Zbl 1468.65117 J. Comput. Appl. Math. 393, Article ID 113519, 16 p. (2021). MSC: 65M06 65M60 26A33 35Q60 92C55 35Q92 35R11 PDFBibTeX XMLCite \textit{T. Xu} et al., J. Comput. Appl. Math. 393, Article ID 113519, 16 p. (2021; Zbl 1468.65117) 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
An, Xingyu; Liu, Fawang; Chen, Shanzhen; Anh, Vo V. Novel numerical techniques for the finite moment log stable computational model for European call option. (English) Zbl 07777659 Numer. Methods Partial Differ. Equations 36, No. 6, 1537-1554 (2020). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{X. An} et al., Numer. Methods Partial Differ. Equations 36, No. 6, 1537--1554 (2020; Zbl 07777659) Full Text: DOI
Liu, Qingxia; Zhuang, Pinghui; Liu, Fawang; Lai, Junjiang; Anh, Vo; Chen, Shanzhen An investigation of radial basis functions for fractional derivatives and their applications. (English) Zbl 1496.76111 Comput. Mech. 65, No. 2, 475-486 (2020). MSC: 76M99 74S40 26A33 PDFBibTeX XMLCite \textit{Q. Liu} et al., Comput. Mech. 65, No. 2, 475--486 (2020; Zbl 1496.76111) Full Text: DOI
Chen, Ruige; Wei, Xiaoli; Liu, Fawang; Anh, Vo V. Multi-term time fractional diffusion equations and novel parameter estimation techniques for chloride ions sub-diffusion in reinforced concrete. (English) Zbl 1462.65102 Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 378, No. 2172, Article ID 20190538, 15 p. (2020). MSC: 65M06 35Q92 35R11 65M12 92C40 PDFBibTeX XMLCite \textit{R. Chen} et al., Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 378, No. 2172, Article ID 20190538, 15 p. (2020; Zbl 1462.65102) Full Text: DOI Link
Xu, Tao; Liu, Fawang; Lü, Shujuan; Anh, Vo V. Finite difference/finite element method for two-dimensional time-space fractional Bloch-Torrey equations with variable coefficients on irregular convex domains. (English) Zbl 1524.65424 Comput. Math. Appl. 80, No. 12, 3173-3192 (2020). MSC: 65M06 65M60 35R11 65M12 26A33 92C55 92C37 65N30 78A60 35Q92 35Q60 PDFBibTeX XMLCite \textit{T. Xu} et al., Comput. Math. Appl. 80, No. 12, 3173--3192 (2020; Zbl 1524.65424) Full Text: DOI
Liu, Fawang; Feng, Libo; Anh, Vo; Li, Jing Unstructured-mesh Galerkin finite element method for the two-dimensional multi-term time-space fractional Bloch-Torrey equations on irregular convex domains. (English) Zbl 1442.65268 Comput. Math. Appl. 78, No. 5, 1637-1650 (2019). MSC: 65M60 65M12 35R11 82C70 PDFBibTeX XMLCite \textit{F. Liu} et al., Comput. Math. Appl. 78, No. 5, 1637--1650 (2019; Zbl 1442.65268) Full Text: DOI
Chen, Ruige; Liu, Fawang; Anh, Vo A fractional alternating-direction implicit method for a multi-term time-space fractional Bloch-Torrey equations in three dimensions. (English) Zbl 1442.65154 Comput. Math. Appl. 78, No. 5, 1261-1273 (2019). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{R. Chen} et al., Comput. Math. Appl. 78, No. 5, 1261--1273 (2019; Zbl 1442.65154) 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
Chen, Ruige; Liu, Fawang; Anh, Vo Numerical methods and analysis for a multi-term time-space variable-order fractional advection-diffusion equations and applications. (English) Zbl 1448.76151 J. Comput. Appl. Math. 352, 437-452 (2019). MSC: 76S05 35Q35 35R11 76M20 65M12 PDFBibTeX XMLCite \textit{R. Chen} et al., J. Comput. Appl. Math. 352, 437--452 (2019; Zbl 1448.76151) Full Text: DOI
Shen, Shujun; Liu, Fawang; Anh, Vo V. The analytical solution and numerical solutions for a two-dimensional multi-term time fractional diffusion and diffusion-wave equation. (English) Zbl 1398.65229 J. Comput. Appl. Math. 345, 515-534 (2019). MSC: 65M20 65L06 65R10 35R11 34A08 PDFBibTeX XMLCite \textit{S. Shen} et al., J. Comput. Appl. Math. 345, 515--534 (2019; Zbl 1398.65229) Full Text: DOI Link
Zhang, H.; Liu, F.; Chen, S.; Anh, V.; Chen, J. Fast numerical simulation of a new time-space fractional option pricing model governing European call option. (English) Zbl 1429.91346 Appl. Math. Comput. 339, 186-198 (2018). MSC: 91G60 65M06 65M12 35R11 35Q91 PDFBibTeX XMLCite \textit{H. Zhang} et al., Appl. Math. Comput. 339, 186--198 (2018; Zbl 1429.91346) Full Text: DOI Link
Fan, Wenping; Jiang, Xiaoyun; Liu, Fawang; Anh, Vo The unstructured mesh finite element method for the two-dimensional multi-term time-space fractional diffusion-wave equation on an irregular convex domain. (English) Zbl 1407.65156 J. Sci. Comput. 77, No. 1, 27-52 (2018). MSC: 65M60 65M12 26A33 65N30 35R11 65M06 35Q35 76A05 PDFBibTeX XMLCite \textit{W. Fan} et al., J. Sci. Comput. 77, No. 1, 27--52 (2018; Zbl 1407.65156) Full Text: DOI
Chen, S.; Liu, F.; Turner, I.; Anh, V. A fast numerical method for two-dimensional Riesz space fractional diffusion equations on a convex bounded region. (English) Zbl 06933818 Appl. Numer. Math. 134, 66-80 (2018). MSC: 65-XX PDFBibTeX XMLCite \textit{S. Chen} et al., Appl. Numer. Math. 134, 66--80 (2018; Zbl 06933818) Full Text: DOI Link
Feng, L. B.; Zhuang, P.; Liu, F.; Turner, I.; Anh, V.; Li, J. A fast second-order accurate method for a two-sided space-fractional diffusion equation with variable coefficients. (English) Zbl 1412.65072 Comput. Math. Appl. 73, No. 6, 1155-1171 (2017). MSC: 65M06 65M12 35R11 65F10 PDFBibTeX XMLCite \textit{L. B. Feng} et al., Comput. Math. Appl. 73, No. 6, 1155--1171 (2017; Zbl 1412.65072) Full Text: DOI
Zhao, Yanmin; Zhang, Yadong; Liu, F.; Turner, I.; Tang, Yifa; Anh, V. Convergence and superconvergence of a fully-discrete scheme for multi-term time fractional diffusion equations. (English) Zbl 1412.65159 Comput. Math. Appl. 73, No. 6, 1087-1099 (2017). MSC: 65M60 65M12 35R11 65D05 PDFBibTeX XMLCite \textit{Y. Zhao} et al., Comput. Math. Appl. 73, No. 6, 1087--1099 (2017; Zbl 1412.65159) Full Text: DOI Link
Zhao, Linlin; Liu, Fawang; Anh, Vo V. Numerical methods for the two-dimensional multi-term time-fractional diffusion equations. (English) Zbl 1397.65150 Comput. Math. Appl. 74, No. 10, 2253-2268 (2017). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{L. Zhao} et al., Comput. Math. Appl. 74, No. 10, 2253--2268 (2017; Zbl 1397.65150) 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
Ming, Chunying; Liu, Fawang; Zheng, Liancun; Turner, Ian; Anh, Vo Analytical solutions of multi-term time fractional differential equations and application to unsteady flows of generalized viscoelastic fluid. (English) Zbl 1398.35277 Comput. Math. Appl. 72, No. 9, 2084-2097 (2016). MSC: 35R11 35Q35 76A10 PDFBibTeX XMLCite \textit{C. Ming} et al., Comput. Math. Appl. 72, No. 9, 2084--2097 (2016; Zbl 1398.35277) Full Text: DOI
Zhuang, Pinghui; Liu, Fawang; Turner, Ian; Anh, Vo Galerkin finite element method and error analysis for the fractional cable equation. (English) Zbl 1343.65125 Numer. Algorithms 72, No. 2, 447-466 (2016). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65M60 65M15 35R11 35L20 65M20 PDFBibTeX XMLCite \textit{P. Zhuang} et al., Numer. Algorithms 72, No. 2, 447--466 (2016; Zbl 1343.65125) Full Text: DOI Link
Hu, Xiuling; Liu, Fawang; Turner, Ian; Anh, Vo An implicit numerical method of a new time distributed-order and two-sided space-fractional advection-dispersion equation. (English) Zbl 1343.65110 Numer. Algorithms 72, No. 2, 393-407 (2016). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65M06 65M12 35R11 35L20 PDFBibTeX XMLCite \textit{X. Hu} et al., Numer. Algorithms 72, No. 2, 393--407 (2016; Zbl 1343.65110) Full Text: DOI Link
Ye, H.; Liu, Fawang; Anh, V. Compact difference scheme for distributed-order time-fractional diffusion-wave equation on bounded domains. (English) Zbl 1349.65353 J. Comput. Phys. 298, 652-660 (2015). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{H. Ye} et al., J. Comput. Phys. 298, 652--660 (2015; Zbl 1349.65353) Full Text: DOI Link
Liu, Fawang; Zhuang, P.; Turner, I.; Anh, V.; Burrage, K. A semi-alternating direction method for a 2-D fractional Fitzhugh-Nagumo monodomain model on an approximate irregular domain. (English) Zbl 1349.65316 J. Comput. Phys. 293, 252-263 (2015). MSC: 65M06 35R11 65M12 92C30 PDFBibTeX XMLCite \textit{F. Liu} et al., J. Comput. Phys. 293, 252--263 (2015; Zbl 1349.65316) Full Text: DOI
Chen, S.; Liu, Fawang; Jiang, X.; Turner, I.; Anh, V. A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients. (English) Zbl 1339.65104 Appl. Math. Comput. 257, 591-601 (2015). MSC: 65M06 65M12 65M22 65T50 PDFBibTeX XMLCite \textit{S. Chen} et al., Appl. Math. Comput. 257, 591--601 (2015; Zbl 1339.65104) 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
Shen, S.; Liu, Fawang; Liu, Q.; Anh, Vo V. Numerical simulation of anomalous infiltration in porous media. (English) Zbl 1310.76121 Numer. Algorithms 68, No. 3, 443-454 (2015). MSC: 76M20 76S05 65M06 PDFBibTeX XMLCite \textit{S. Shen} et al., Numer. Algorithms 68, No. 3, 443--454 (2015; Zbl 1310.76121) Full Text: DOI Link
Liu, F.; Zhuang, P.; Turner, I.; Burrage, K.; Anh, V. A new fractional finite volume method for solving the fractional diffusion equation. (English) Zbl 1429.65213 Appl. Math. Modelling 38, No. 15-16, 3871-3878 (2014). MSC: 65M08 35R11 PDFBibTeX XMLCite \textit{F. Liu} et al., Appl. Math. Modelling 38, No. 15--16, 3871--3878 (2014; Zbl 1429.65213) Full Text: DOI
Chen, J.; Liu, F.; Liu, Q.; Chen, X.; Anh, V.; Turner, I.; Burrage, K. Numerical simulation for the three-dimension fractional sub-diffusion equation. (English) Zbl 1429.65179 Appl. Math. Modelling 38, No. 15-16, 3695-3705 (2014). MSC: 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{J. Chen} et al., Appl. Math. Modelling 38, No. 15--16, 3695--3705 (2014; Zbl 1429.65179) Full Text: DOI
Ye, H.; Liu, Fawang; Anh, V.; Turner, I. Maximum principle and numerical method for the multi-term time-space Riesz-Caputo fractional differential equations. (English) Zbl 1364.35428 Appl. Math. Comput. 227, 531-540 (2014). MSC: 35R11 35B50 65M99 PDFBibTeX XMLCite \textit{H. Ye} et al., Appl. Math. Comput. 227, 531--540 (2014; Zbl 1364.35428) Full Text: DOI
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
Zhang, Hongmei; Liu, Fawang; Zhuang, P.; Turner, I.; Anh, V. Numerical analysis of a new space-time variable fractional order advection-dispersion equation. (English) Zbl 1334.65143 Appl. Math. Comput. 242, 541-550 (2014). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{H. Zhang} et al., Appl. Math. Comput. 242, 541--550 (2014; Zbl 1334.65143) Full Text: DOI
Shen, S.; Liu, Fawang; Anh, V.; Turner, I.; Chen, J. A characteristic difference method for the variable-order fractional advection-diffusion equation. (English) Zbl 1296.65114 J. Appl. Math. Comput. 42, No. 1-2, 371-386 (2013). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{S. Shen} et al., J. Appl. Math. Comput. 42, No. 1--2, 371--386 (2013; Zbl 1296.65114) Full Text: DOI
Chen, Chang-Ming; Liu, Fawang; Turner, I.; Anh, V.; Chen, Y. Numerical approximation for a variable-order nonlinear reaction-subdiffusion equation. (English) Zbl 1278.65121 Numer. Algorithms 63, No. 2, 265-290 (2013). Reviewer: Snezhana Gocheva-Ilieva (Plovdiv) MSC: 65M06 65M12 35R11 35K57 PDFBibTeX XMLCite \textit{C.-M. Chen} et al., Numer. Algorithms 63, No. 2, 265--290 (2013; Zbl 1278.65121) Full Text: DOI
Chen, J.; Liu, Fawang; Anh, V.; Shen, S.; Liu, Q.; Liao, C. The analytical solution and numerical solution of the fractional diffusion-wave equation with damping. (English) Zbl 1290.35306 Appl. Math. Comput. 219, No. 4, 1737-1748 (2012). MSC: 35R11 26A33 PDFBibTeX XMLCite \textit{J. Chen} et al., Appl. Math. Comput. 219, No. 4, 1737--1748 (2012; Zbl 1290.35306) Full Text: DOI Link
Shen, S.; Liu, Fawang; Chen, J.; Turner, I.; Anh, V. Numerical techniques for the variable-order time fractional diffusion equation. (English) Zbl 1280.65089 Appl. Math. Comput. 218, No. 22, 10861-10870 (2012). MSC: 65M06 35K05 35R11 65M12 PDFBibTeX XMLCite \textit{S. Shen} et al., Appl. Math. Comput. 218, No. 22, 10861--10870 (2012; Zbl 1280.65089) Full Text: DOI Link
Chen, Chang-Ming; Liu, Fawang; Anh, V.; Turner, I. Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation. (English) Zbl 1241.65077 Math. Comput. 81, No. 277, 345-366 (2012). Reviewer: Fernando Casas (Castellon) MSC: 65M20 65L06 35K20 35R11 65M12 PDFBibTeX XMLCite \textit{C.-M. Chen} et al., Math. Comput. 81, No. 277, 345--366 (2012; Zbl 1241.65077) Full Text: DOI
Chen, Chang-Ming; Liu, Fawang; Turner, I.; Anh, V. Numerical methods with fourth-order spatial accuracy for variable-order nonlinear Stokes first problem for a heated generalized second grade fluid. (English) Zbl 1228.65207 Comput. Math. Appl. 62, No. 3, 971-986 (2011). MSC: 65N06 76M25 35R11 26A33 45K05 76D07 PDFBibTeX XMLCite \textit{C.-M. Chen} et al., Comput. Math. Appl. 62, No. 3, 971--986 (2011; Zbl 1228.65207) Full Text: DOI
Liu, Q.; Liu, Fawang; Turner, I.; Anh, V. Finite element approximation for a modified anomalous subdiffusion equation. (English) Zbl 1221.65257 Appl. Math. Modelling 35, No. 8, 4103-4116 (2011). MSC: 65M60 35K20 35R11 65M12 PDFBibTeX XMLCite \textit{Q. Liu} et al., Appl. Math. Modelling 35, No. 8, 4103--4116 (2011; Zbl 1221.65257) Full Text: DOI
Chen, Shi Ping; Liu, F.; Anh, V. A novel implicit finite difference method for the one-dimensional fractional percolation equation. (English) Zbl 1429.65180 Numer. Algorithms 56, No. 4, 517-535 (2011). MSC: 65M06 35R11 35Q35 65M12 76M20 PDFBibTeX XMLCite \textit{S. P. Chen} et al., Numer. Algorithms 56, No. 4, 517--535 (2011; Zbl 1429.65180) Full Text: DOI
Shen, Shujun; Liu, Fawang; Anh, Vo Numerical approximations and solution techniques for the space-time Riesz-Caputo fractional advection-diffusion equation. (English) Zbl 1214.65046 Numer. Algorithms 56, No. 3, 383-403 (2011). Reviewer: Gisbert Stoyan (Budapest) MSC: 65M06 65M12 35K15 35K20 35R11 PDFBibTeX XMLCite \textit{S. Shen} et al., Numer. Algorithms 56, No. 3, 383--403 (2011; Zbl 1214.65046) Full Text: DOI
Chen, Chang-Ming; Liu, Fawang; Anh, V.; Turner, I. Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term. (English) Zbl 1227.65072 Appl. Math. Comput. 217, No. 12, 5729-5742 (2011). Reviewer: Thomas Sonar (Braunschweig) MSC: 65M06 65M12 35K55 PDFBibTeX XMLCite \textit{C.-M. Chen} et al., Appl. Math. Comput. 217, No. 12, 5729--5742 (2011; Zbl 1227.65072) Full Text: DOI Link
Zhang, H.; Liu, F.; Anh, V. Galerkin finite element approximation of symmetric space-fractional partial differential equations. (English) Zbl 1206.65234 Appl. Math. Comput. 217, No. 6, 2534-2545 (2010). Reviewer: Pavol Chocholatý (Bratislava) MSC: 65M60 PDFBibTeX XMLCite \textit{H. Zhang} et al., Appl. Math. Comput. 217, No. 6, 2534--2545 (2010; Zbl 1206.65234) Full Text: DOI
Ilic, M.; Turner, I. W.; Liu, Fawang; Anh, V. Analytical and numerical solutions of a one-dimensional fractional-in-space diffusion equation in a composite medium. (English) Zbl 1193.65168 Appl. Math. Comput. 216, No. 8, 2248-2262 (2010). MSC: 65M55 35K20 65M70 35R11 PDFBibTeX XMLCite \textit{M. Ilic} et al., Appl. Math. Comput. 216, No. 8, 2248--2262 (2010; Zbl 1193.65168) Full Text: DOI
Chen, Chang-Ming; Liu, Fawang; Turner, Ian; Anh, Vo Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation. (English) Zbl 1191.65116 Numer. Algorithms 54, No. 1, 1-21 (2010). Reviewer: Marius Ghergu (Dublin) MSC: 65M12 65M06 35K05 PDFBibTeX XMLCite \textit{C.-M. Chen} et al., Numer. Algorithms 54, No. 1, 1--21 (2010; Zbl 1191.65116) Full Text: DOI Link
Chen, S.; Liu, Fawang; Zhuang, P.; Anh, V. Finite difference approximations for the fractional Fokker-Planck equation. (English) Zbl 1167.65419 Appl. Math. Modelling 33, No. 1, 256-273 (2009). MSC: 65M06 26A33 35K55 PDFBibTeX XMLCite \textit{S. Chen} et al., Appl. Math. Modelling 33, No. 1, 256--273 (2009; Zbl 1167.65419) Full Text: DOI
Lin, R.; Liu, Fawang; Anh, V.; Turner, I. Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation. (English) Zbl 1171.65101 Appl. Math. Comput. 212, No. 2, 435-445 (2009). Reviewer: Ivan Secrieru (Chişinău) MSC: 65R20 45K05 45G10 35K57 26A33 65M06 65M12 PDFBibTeX XMLCite \textit{R. Lin} et al., Appl. Math. Comput. 212, No. 2, 435--445 (2009; Zbl 1171.65101) Full Text: DOI Link
Chen, Changming; Liu, Fawang; Anh, V. A Fourier method and an extrapolation technique for Stokes’ first problem for a heated generalized second-grade fluid with fractional derivative. (English) Zbl 1153.76049 J. Comput. Appl. Math. 223, No. 2, 777-789 (2009). MSC: 76M25 76A10 80A20 PDFBibTeX XMLCite \textit{C. Chen} et al., J. Comput. Appl. Math. 223, No. 2, 777--789 (2009; Zbl 1153.76049) Full Text: DOI Link
Chen, J.; Liu, Fawang; Turner, I.; Anh, V. The fundamental and numerical solutions of the Riesz space-fractional reaction-dispersion equation. (English) Zbl 1179.35029 ANZIAM J. 50, No. 1, 45-57 (2008). Reviewer: V. S. Borkar (Mumbai) MSC: 35A35 35K57 35A08 35A22 65M06 35R11 PDFBibTeX XMLCite \textit{J. Chen} et al., ANZIAM J. 50, No. 1, 45--57 (2008; Zbl 1179.35029) Full Text: DOI
Ilić, M.; Turner, I. W.; Anh, V. A numerical solution using an adaptively preconditioned Lanczos method for a class of linear systems related with the fractional Poisson equation. (English) Zbl 1162.65015 J. Appl. Math. Stochastic Anal. 2008, Article ID 104525, 26 p. (2008). MSC: 65F10 65F35 35J05 45K05 65R20 26A33 PDFBibTeX XMLCite \textit{M. Ilić} et al., J. Appl. Math. Stochastic Anal. 2008, Article ID 104525, 26 p. (2008; Zbl 1162.65015) Full Text: DOI EuDML
Chen, Changming; Liu, Fawang; Anh, V. Numerical analysis of the Rayleigh-Stokes problem for a heated generalized second-grade fluid with fractional derivatives. (English) Zbl 1153.76010 Appl. Math. Comput. 204, No. 1, 340-351 (2008). MSC: 76A05 76M20 PDFBibTeX XMLCite \textit{C. Chen} et al., Appl. Math. Comput. 204, No. 1, 340--351 (2008; Zbl 1153.76010) Full Text: DOI
Shen, S.; Liu, Fawang; Anh, V. Fundamental solution and discrete random walk model for a time-space fractional diffusion equation of distributed order. (English) Zbl 1157.65520 J. Appl. Math. Comput. 28, No. 1-2, 147-164 (2008). MSC: 65R20 45K05 26A33 65M06 65G50 46F10 60H25 PDFBibTeX XMLCite \textit{S. Shen} et al., J. Appl. Math. Comput. 28, No. 1--2, 147--164 (2008; Zbl 1157.65520) Full Text: DOI Link
Chen, J.; Liu, Fawang; Anh, V. Analytical solution for the time-fractional telegraph equation by the method of separating variables. (English) Zbl 1138.35373 J. Math. Anal. Appl. 338, No. 2, 1364-1377 (2008). MSC: 35L70 35S05 35L20 PDFBibTeX XMLCite \textit{J. Chen} et al., J. Math. Anal. Appl. 338, No. 2, 1364--1377 (2008; Zbl 1138.35373) Full Text: DOI
Liu, Fawang; Zhuang, P.; Anh, V.; Turner, I.; Burrage, K. Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation. (English) Zbl 1193.76093 Appl. Math. Comput. 191, No. 1, 12-20 (2007). MSC: 76M20 65M06 PDFBibTeX XMLCite \textit{F. Liu} et al., Appl. Math. Comput. 191, No. 1, 12--20 (2007; Zbl 1193.76093) Full Text: DOI
Chen, Chang-Ming; Liu, Fawang; Turner, I.; Anh, V. A Fourier method for the fractional diffusion equation describing sub-diffusion. (English) Zbl 1165.65053 J. Comput. Phys. 227, No. 2, 886-897 (2007). Reviewer: Pat Lumb (Chester) MSC: 65M12 65M70 35B35 PDFBibTeX XMLCite \textit{C.-M. Chen} et al., J. Comput. Phys. 227, No. 2, 886--897 (2007; Zbl 1165.65053) Full Text: DOI Link
Zhang, H.; Liu, Fawang; Anh, V. Numerical approximation of Lévy-Feller diffusion equation and its probability interpretation. (English) Zbl 1125.26014 J. Comput. Appl. Math. 206, No. 2, 1098-1115 (2007). Reviewer: James Adedayo Oguntuase (Abeokuta) MSC: 26A33 34K28 60G57 PDFBibTeX XMLCite \textit{H. Zhang} et al., J. Comput. Appl. Math. 206, No. 2, 1098--1115 (2007; Zbl 1125.26014) Full Text: DOI
Liu, Q.; Liu, Fawang; Turner, I.; Anh, V. Approximation of the Lévy-Feller advection-dispersion process by random walk and finite difference method. (English) Zbl 1112.65006 J. Comput. Phys. 222, No. 1, 57-70 (2007). Reviewer: Henri Schurz (Carbondale) MSC: 65C30 35K50 60H30 65M06 65M12 60H15 26A33 60G50 PDFBibTeX XMLCite \textit{Q. Liu} et al., J. Comput. Phys. 222, No. 1, 57--70 (2007; Zbl 1112.65006) Full Text: DOI
Shen, S.; Liu, Fawang; Anh, V.; Turner, I. Detailed analysis of a conservative difference approximation for the time fractional diffusion equation. (English) Zbl 1111.65115 J. Appl. Math. Comput. 22, No. 3, 1-19 (2006). Reviewer: Neville Ford (Chester) MSC: 65R20 45J05 26A33 PDFBibTeX XMLCite \textit{S. Shen} et al., J. Appl. Math. Comput. 22, No. 3, 1--19 (2006; Zbl 1111.65115) Full Text: DOI
Liu, Fawang; Anh, V. V.; Turner, I.; Bajracharya, K.; Huxley, W. J.; Su, N. A finite volume simulation model for saturated–unsaturated flow and application to Gooburrum, Bundaberg, Queensland, Australia. (English) Zbl 1163.76392 Appl. Math. Modelling 30, No. 4, 352-366 (2006). MSC: 76M12 PDFBibTeX XMLCite \textit{F. Liu} et al., Appl. Math. Modelling 30, No. 4, 352--366 (2006; Zbl 1163.76392) Full Text: DOI
Liu, Fawang; Anh, V.; Turner, I. Numerical solution of the space fractional Fokker-Planck equation. (English) Zbl 1036.82019 J. Comput. Appl. Math. 166, No. 1, 209-219 (2004). MSC: 82C31 26A33 PDFBibTeX XMLCite \textit{F. Liu} et al., J. Comput. Appl. Math. 166, No. 1, 209--219 (2004; Zbl 1036.82019) Full Text: DOI
Liu, Fawang; Turner, I.; Anh, V.; Su, N. A two-dimensional finite volume method for transient simulation of time- and scale-dependent transport in heterogeneous aquifer systems. (English) Zbl 1145.76407 J. Appl. Math. Comput. 11, No. 1-2, 215-241 (2003). MSC: 76M12 76S05 86-08 65M20 86A05 PDFBibTeX XMLCite \textit{F. Liu} et al., J. Appl. Math. Comput. 11, No. 1--2, 215--241 (2003; Zbl 1145.76407) Full Text: DOI