Yu, Qiang; Turner, Ian; Liu, Fawang; Moroney, Timothy A study of distributed-order time fractional diffusion models with continuous distribution weight functions. (English) Zbl 07779715 Numer. Methods Partial Differ. Equations 39, No. 1, 383-420 (2023). MSC: 65M06 65M12 65D32 44A10 35B40 PDFBibTeX XMLCite \textit{Q. Yu} et al., Numer. Methods Partial Differ. Equations 39, No. 1, 383--420 (2023; Zbl 07779715) Full Text: DOI
Chen, Xuejuan; Chen, Jinghua; Liu, Fawang; Sun, Zhi-zhong A fourth-order accurate numerical method for the distributed-order Riesz space fractional diffusion equation. (English) Zbl 07776962 Numer. Methods Partial Differ. Equations 39, No. 2, 1266-1286 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{X. Chen} et al., Numer. Methods Partial Differ. Equations 39, No. 2, 1266--1286 (2023; Zbl 07776962) Full Text: DOI
Feng, Libo; Turner, Ian; Moroney, Timothy; Liu, Fawang Fractional potential: a new perspective on the fractional Laplacian problem on bounded domains. (English) Zbl 1523.35282 Commun. Nonlinear Sci. Numer. Simul. 125, Article ID 107368, 19 p. (2023). MSC: 35R11 35A35 35K20 PDFBibTeX XMLCite \textit{L. Feng} et al., Commun. Nonlinear Sci. Numer. Simul. 125, Article ID 107368, 19 p. (2023; Zbl 1523.35282) Full Text: DOI
Gao, Xinghua; Liu, Fawang; Li, Hong; Liu, Yang; Turner, Ian; Yin, Baoli A novel finite element method for the distributed-order time fractional Cable equation in two dimensions. (English) Zbl 1447.65072 Comput. Math. Appl. 80, No. 5, 923-939 (2020). MSC: 65M60 65M06 65M12 35R11 26A33 92C20 35Q92 PDFBibTeX XMLCite \textit{X. Gao} et al., Comput. Math. Appl. 80, No. 5, 923--939 (2020; Zbl 1447.65072) Full Text: DOI
Li, Lang; Liu, Fawang; Feng, Libo; Turner, Ian A Galerkin finite element method for the modified distributed-order anomalous sub-diffusion equation. (English) Zbl 1440.65142 J. Comput. Appl. Math. 368, Article ID 112589, 18 p. (2020). MSC: 65M60 65N30 65M06 65D30 65M12 65M15 26A33 35R11 PDFBibTeX XMLCite \textit{L. Li} et al., J. Comput. Appl. Math. 368, Article ID 112589, 18 p. (2020; Zbl 1440.65142) Full Text: DOI
Feng, Libo; Liu, Fawang; Turner, Ian Finite difference/finite element method for a novel 2D multi-term time-fractional mixed sub-diffusion and diffusion-wave equation on convex domains. (English) Zbl 1464.65119 Commun. Nonlinear Sci. Numer. Simul. 70, 354-371 (2019). MSC: 65M60 PDFBibTeX XMLCite \textit{L. Feng} et al., Commun. Nonlinear Sci. Numer. Simul. 70, 354--371 (2019; Zbl 1464.65119) 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
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
Jiang, H.; Liu, Fawang; Turner, I.; Burrage, K. Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain. (English) Zbl 1268.35124 Comput. Math. Appl. 64, No. 10, 3377-3388 (2012). MSC: 35R11 35C10 PDFBibTeX XMLCite \textit{H. Jiang} et al., Comput. Math. Appl. 64, No. 10, 3377--3388 (2012; Zbl 1268.35124) Full Text: DOI
Liu, F.; Zhuang, P.; Burrage, K. Numerical methods and analysis for a class of fractional advection-dispersion models. (English) Zbl 1268.65124 Comput. Math. Appl. 64, No. 10, 2990-3007 (2012). MSC: 65M12 35R11 45K05 PDFBibTeX XMLCite \textit{F. Liu} et al., Comput. Math. Appl. 64, No. 10, 2990--3007 (2012; Zbl 1268.65124) 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
Yang, Q.; Liu, Fawang; Turner, I. Numerical methods for fractional partial differential equations with Riesz space fractional derivatives. (English) Zbl 1185.65200 Appl. Math. Modelling 34, No. 1, 200-218 (2010). MSC: 65M99 26A33 35R11 PDFBibTeX XMLCite \textit{Q. Yang} et al., Appl. Math. Modelling 34, No. 1, 200--218 (2010; Zbl 1185.65200) Full Text: DOI
Chen, Chang-Ming; Liu, F. A numerical approximation method for solving a three-dimensional space Galilei invariant fractional advection-diffusion equation. (English) Zbl 1177.26009 J. Appl. Math. Comput. 30, No. 1-2, 219-236 (2009). MSC: 26A33 65M12 65M06 PDFBibTeX XMLCite \textit{C.-M. Chen} and \textit{F. Liu}, J. Appl. Math. Comput. 30, No. 1--2, 219--236 (2009; Zbl 1177.26009) 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, 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
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
Huang, F.; Liu, Fawang The space-time fractional diffusion equation with Caputo derivatives. (English) Zbl 1085.35003 J. Appl. Math. Comput. 19, No. 1-2, 179-190 (2005). MSC: 35A08 26A33 49K20 44A10 35S10 PDFBibTeX XMLCite \textit{F. Huang} and \textit{F. Liu}, J. Appl. Math. Comput. 19, No. 1--2, 179--190 (2005; Zbl 1085.35003) Full Text: DOI
Huang, F.; Liu, Fawang The fundamental solution of the space-time fractional advection-dispersion equation. (English) Zbl 1086.35003 J. Appl. Math. Comput. 18, No. 1-2, 339-350 (2005). MSC: 35A08 35K57 26A33 49K20 44A10 PDFBibTeX XMLCite \textit{F. Huang} and \textit{F. Liu}, J. Appl. Math. Comput. 18, No. 1--2, 339--350 (2005; Zbl 1086.35003) 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; Anh, V. V.; Turner, I.; Zhuang, P. Time fractional advection-dispersion equation. (English) Zbl 1068.26006 J. Appl. Math. Comput. 13, No. 1-2, 233-245 (2003). Reviewer: Rudolf Gorenflo (Berlin) MSC: 26A33 33D15 44A10 44A15 45K05 35K57 PDFBibTeX XMLCite \textit{F. Liu} et al., J. Appl. Math. Comput. 13, No. 1--2, 233--245 (2003; Zbl 1068.26006) Full Text: DOI