Zhao, Jingjun; Zhao, Wenjiao; Xu, Yang Hybridizable discontinuous Galerkin methods for space-time fractional advection-dispersion equations. (English) Zbl 1511.65107 Appl. Math. Comput. 442, Article ID 127745, 21 p. (2023). MSC: 65M60 35R11 65M12 65R20 PDFBibTeX XMLCite \textit{J. Zhao} et al., Appl. Math. Comput. 442, Article ID 127745, 21 p. (2023; Zbl 1511.65107) Full Text: DOI
Yu, Jian-Wei; Zhang, Chun-Hua; Huang, Xin; Wang, Xiang A class of preconditioner for solving the Riesz distributed-order nonlinear space-fractional diffusion equations. (English) Zbl 1505.65251 Japan J. Ind. Appl. Math. 40, No. 1, 537-562 (2023). MSC: 65M06 65N06 65T50 65F08 65M12 41A25 15B05 15A18 35R11 PDFBibTeX XMLCite \textit{J.-W. Yu} et al., Japan J. Ind. Appl. Math. 40, No. 1, 537--562 (2023; Zbl 1505.65251) Full Text: DOI
Gan, Di; Zhang, Guo-Feng Efficient ADI schemes and preconditioning for a class of high-dimensional spatial fractional diffusion equations with variable diffusion coefficients. (English) Zbl 1505.65284 J. Comput. Appl. Math. 423, Article ID 114938, 15 p. (2023). MSC: 65N06 65M06 65F08 65F10 65F55 65M12 65N12 15B05 65T50 26A33 35R11 PDFBibTeX XMLCite \textit{D. Gan} and \textit{G.-F. Zhang}, J. Comput. Appl. Math. 423, Article ID 114938, 15 p. (2023; Zbl 1505.65284) Full Text: DOI
Ivani, Sara; Jalilian, Reza An non-polynomial spline approximation for fractional Bagley-Torvik equation. (Persian. English summary) Zbl 07588271 JAMM, J. Adv. Math. Model. 12, No. 2, 248-270 (2022). MSC: 65-XX 74-XX PDFBibTeX XMLCite \textit{S. Ivani} and \textit{R. Jalilian}, JAMM, J. Adv. Math. Model. 12, No. 2, 248--270 (2022; Zbl 07588271) Full Text: DOI
Fahimi-khalilabad, Iraj; Irandoust-pakchin, Safar; Abdi-mazraeh, Somayeh High-order finite difference method based on linear barycentric rational interpolation for Caputo type sub-diffusion equation. (English) Zbl 07538450 Math. Comput. Simul. 199, 60-80 (2022). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{I. Fahimi-khalilabad} et al., Math. Comput. Simul. 199, 60--80 (2022; Zbl 07538450) Full Text: DOI
Meng, Yahui; Li, Botong; Si, Xinhui Numerical analysis of fractional viscoelastic fluid problem solved by finite difference scheme. (English) Zbl 1504.65179 Comput. Math. Appl. 113, 225-242 (2022). MSC: 65M06 35Q35 65M12 76A10 PDFBibTeX XMLCite \textit{Y. Meng} et al., Comput. Math. Appl. 113, 225--242 (2022; Zbl 1504.65179) Full Text: DOI
Meng, Yahui; Li, Botong; Si, Xinhui; Chen, Xuehui; Liu, Fawang On the process of filtration of fractional viscoelastic liquid food. (English) Zbl 1521.76836 Commun. Theor. Phys. 73, No. 4, Article ID 045004, 16 p. (2021). MSC: 76S05 65M06 35R11 76A10 76A05 65M12 PDFBibTeX XMLCite \textit{Y. Meng} et al., Commun. Theor. Phys. 73, No. 4, Article ID 045004, 16 p. (2021; Zbl 1521.76836) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi A Galerkin meshless reproducing kernel particle method for numerical solution of neutral delay time-space distributed-order fractional damped diffusion-wave equation. (English) Zbl 1486.65157 Appl. Numer. Math. 169, 44-63 (2021). MSC: 65M60 65M06 65N30 65M75 65M12 26A33 35R11 35R07 35R10 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Appl. Numer. Math. 169, 44--63 (2021; Zbl 1486.65157) Full Text: DOI
Emadifar, Homan; Jalilian, Reza An exponential spline approximation for fractional Bagley-Torvik equation. (English) Zbl 1493.65028 Bound. Value Probl. 2020, Paper No. 20, 20 p. (2020). MSC: 65D07 65L10 34A08 PDFBibTeX XMLCite \textit{H. Emadifar} and \textit{R. Jalilian}, Bound. Value Probl. 2020, Paper No. 20, 20 p. (2020; Zbl 1493.65028) Full Text: DOI
Goufo, Emile F. Doungmo; Khumalo, M.; Toudjeu, Ignace Tchangou; Yildirim, Ahmet Mathematical application of a non-local operator in language evolutionary theory. (English) Zbl 1495.92045 Chaos Solitons Fractals 131, Article ID 109541, 11 p. (2020). MSC: 92D15 91F20 PDFBibTeX XMLCite \textit{E. F. D. Goufo} et al., Chaos Solitons Fractals 131, Article ID 109541, 11 p. (2020; Zbl 1495.92045) Full Text: DOI
Yeganeh, Somayeh; Mokhtari, Reza; Hesthaven, Jan S. A local discontinuous Galerkin method for two-dimensional time fractional diffusion equations. (English) Zbl 1476.65260 Commun. Appl. Math. Comput. 2, No. 4, 689-709 (2020). MSC: 65M60 65M12 PDFBibTeX XMLCite \textit{S. Yeganeh} et al., Commun. Appl. Math. Comput. 2, No. 4, 689--709 (2020; Zbl 1476.65260) Full Text: DOI
Abdi, Narjes; Aminikhah, Hossein; Refahi Sheikhani, Amir Hossein; Alavi, Javad A high-order compact alternating direction implicit method for solving the 3D time-fractional diffusion equation with the Caputo-Fabrizio operator. (English) Zbl 1473.65089 Math. Sci., Springer 14, No. 4, 359-373 (2020). MSC: 65M06 65M12 PDFBibTeX XMLCite \textit{N. Abdi} et al., Math. Sci., Springer 14, No. 4, 359--373 (2020; Zbl 1473.65089) Full Text: DOI
Goufo, Emile Franc Doungmo; Atangana, Abdon Dynamics of traveling waves of variable order hyperbolic Liouville equation: regulation and control. (English) Zbl 1439.35118 Discrete Contin. Dyn. Syst., Ser. S 13, No. 3, 645-662 (2020). MSC: 35C07 35L71 35L15 26A33 65L20 82C70 33F05 PDFBibTeX XMLCite \textit{E. F. D. Goufo} and \textit{A. Atangana}, Discrete Contin. Dyn. Syst., Ser. S 13, No. 3, 645--662 (2020; Zbl 1439.35118) Full Text: DOI
Li, Botong; Liu, Fawang Boundary layer flows of viscoelastic fluids over a non-uniform permeable surface. (English) Zbl 1437.65104 Comput. Math. Appl. 79, No. 8, 2376-2387 (2020). MSC: 65M06 65M12 76M20 26A33 35R11 76A10 PDFBibTeX XMLCite \textit{B. Li} and \textit{F. Liu}, Comput. Math. Appl. 79, No. 8, 2376--2387 (2020; Zbl 1437.65104) Full Text: DOI
Salehi, Rezvan Two implicit meshless finite point schemes for the two-dimensional distributed-order fractional equation. (English) Zbl 1434.65209 Comput. Methods Appl. Math. 19, No. 4, 813-831 (2019). MSC: 65M70 65M12 65M15 35R11 60G22 PDFBibTeX XMLCite \textit{R. Salehi}, Comput. Methods Appl. Math. 19, No. 4, 813--831 (2019; Zbl 1434.65209) Full Text: DOI
Wei, Leilei; Liu, Lijie; Sun, Huixia Stability and convergence of a local discontinuous Galerkin method for the fractional diffusion equation with distributed order. (English) Zbl 1422.65271 J. Appl. Math. Comput. 59, No. 1-2, 323-341 (2019). MSC: 65M60 65M12 65M06 35S10 65M15 35R11 PDFBibTeX XMLCite \textit{L. Wei} et al., J. Appl. Math. Comput. 59, No. 1--2, 323--341 (2019; Zbl 1422.65271) Full Text: DOI
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
Li, Changpin; Yi, Qian Finite difference method for two-dimensional nonlinear time-fractional subdiffusion equation. (English) Zbl 1428.65010 Fract. Calc. Appl. Anal. 21, No. 4, 1046-1072 (2018). MSC: 65M06 26A33 35R11 65M12 15A18 65F15 PDFBibTeX XMLCite \textit{C. Li} and \textit{Q. Yi}, Fract. Calc. Appl. Anal. 21, No. 4, 1046--1072 (2018; Zbl 1428.65010) Full Text: DOI
Liang, Xiao; Khaliq, Abdul Q. M. An efficient Fourier spectral exponential time differencing method for the space-fractional nonlinear Schrödinger equations. (English) Zbl 1419.65083 Comput. Math. Appl. 75, No. 12, 4438-4457 (2018). MSC: 65M70 65M12 35R11 35Q55 35Q41 65M06 PDFBibTeX XMLCite \textit{X. Liang} and \textit{A. Q. M. Khaliq}, Comput. Math. Appl. 75, No. 12, 4438--4457 (2018; Zbl 1419.65083) Full Text: DOI
Hu, Jiahui; Wang, Jungang; Nie, Yufeng Numerical algorithms for multidimensional time-fractional wave equation of distributed-order with a nonlinear source term. (English) Zbl 1448.65130 Adv. Difference Equ. 2018, Paper No. 352, 30 p. (2018). MSC: 65M12 65M06 65M70 35R11 26A33 PDFBibTeX XMLCite \textit{J. Hu} et al., Adv. Difference Equ. 2018, Paper No. 352, 30 p. (2018; Zbl 1448.65130) Full Text: DOI
Zaky, M. A.; Baleanu, D.; Alzaidy, J. F.; Hashemizadeh, E. Operational matrix approach for solving the variable-order nonlinear Galilei invariant advection-diffusion equation. (English) Zbl 1445.65042 Adv. Difference Equ. 2018, Paper No. 102, 11 p. (2018). MSC: 65M70 65M06 65M12 35R11 26A33 PDFBibTeX XMLCite \textit{M. A. Zaky} et al., Adv. Difference Equ. 2018, Paper No. 102, 11 p. (2018; Zbl 1445.65042) Full Text: DOI
Aboelenen, Tarek Local discontinuous Galerkin method for distributed-order time and space-fractional convection-diffusion and Schrödinger-type equations. (English) Zbl 1398.35261 Nonlinear Dyn. 92, No. 2, 395-413 (2018). MSC: 35R11 65M60 65M12 PDFBibTeX XMLCite \textit{T. Aboelenen}, Nonlinear Dyn. 92, No. 2, 395--413 (2018; Zbl 1398.35261) Full Text: DOI arXiv
Saw, Vijay; Kumar, Sushil Fourth kind shifted Chebyshev polynomials for solving space fractional order advection-dispersion equation based on collocation method and finite difference approximation. (English) Zbl 1402.65128 Int. J. Appl. Comput. Math. 4, No. 3, Paper No. 82, 17 p. (2018). MSC: 65M70 65L12 41A50 65M12 65M15 35R11 35Q35 76S05 PDFBibTeX XMLCite \textit{V. Saw} and \textit{S. Kumar}, Int. J. Appl. Comput. Math. 4, No. 3, Paper No. 82, 17 p. (2018; Zbl 1402.65128) Full Text: DOI
Arshad, Sadia; Bu, Weiping; Huang, Jianfei; Tang, Yifa; Zhao, Yue Finite difference method for time-space linear and nonlinear fractional diffusion equations. (English) Zbl 1387.65080 Int. J. Comput. Math. 95, No. 1, 202-217 (2018). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{S. Arshad} et al., Int. J. Comput. Math. 95, No. 1, 202--217 (2018; Zbl 1387.65080) Full Text: DOI
Baeumer, Boris; Kovács, Mihály; Meerschaert, Mark M.; Sankaranarayanan, Harish Reprint of: boundary conditions for fractional diffusion. (English) Zbl 06867170 J. Comput. Appl. Math. 339, 414-430 (2018). MSC: 35R11 26A33 65M06 65M12 82C31 PDFBibTeX XMLCite \textit{B. Baeumer} et al., J. Comput. Appl. Math. 339, 414--430 (2018; Zbl 06867170) Full Text: DOI
Doungmo Goufo, Emile F.; Nieto, Juan J. Attractors for fractional differential problems of transition to turbulent flows. (English) Zbl 1440.76038 J. Comput. Appl. Math. 339, 329-342 (2018). MSC: 76F06 34A08 33F05 37D45 PDFBibTeX XMLCite \textit{E. F. Doungmo Goufo} and \textit{J. J. Nieto}, J. Comput. Appl. Math. 339, 329--342 (2018; Zbl 1440.76038) Full Text: DOI
Wei, Leilei Analysis of a new finite difference/local discontinuous Galerkin method for the fractional Cattaneo equation. (English) Zbl 1395.65035 Numer. Algorithms 77, No. 3, 675-690 (2018). Reviewer: Marius Ghergu (Dublin) MSC: 65M06 65M60 35Q79 35R11 65M12 65M15 PDFBibTeX XMLCite \textit{L. Wei}, Numer. Algorithms 77, No. 3, 675--690 (2018; Zbl 1395.65035) Full Text: DOI
Baeumer, Boris; Kovács, Mihály; Meerschaert, Mark M.; Sankaranarayanan, Harish Boundary conditions for fractional diffusion. (English) Zbl 1386.35424 J. Comput. Appl. Math. 336, 408-424 (2018). MSC: 35R11 65M06 65M12 PDFBibTeX XMLCite \textit{B. Baeumer} et al., J. Comput. Appl. Math. 336, 408--424 (2018; Zbl 1386.35424) Full Text: DOI arXiv
Wei, Leilei Analysis of a new finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation. (English) Zbl 1411.65135 Appl. Math. Comput. 304, 180-189 (2017). MSC: 65M60 35R11 35S10 65M12 PDFBibTeX XMLCite \textit{L. Wei}, Appl. Math. Comput. 304, 180--189 (2017; Zbl 1411.65135) Full Text: DOI arXiv
Qiu, Meilan; Mei, Liquan; Li, Dewang Fully discrete local discontinuous Galerkin approximation for time-space fractional subdiffusion/superdiffusion equations. (English) Zbl 1404.65179 Adv. Math. Phys. 2017, Article ID 4961797, 20 p. (2017). MSC: 65M60 65M06 65M12 35R11 76R50 35Q35 PDFBibTeX XMLCite \textit{M. Qiu} et al., Adv. Math. Phys. 2017, Article ID 4961797, 20 p. (2017; Zbl 1404.65179) Full Text: DOI
Owolabi, Kolade M.; Atangana, Abdon Analysis and application of new fractional Adams-Bashforth scheme with Caputo-Fabrizio derivative. (English) Zbl 1380.65120 Chaos Solitons Fractals 105, 111-119 (2017). MSC: 65L05 34A08 65L20 PDFBibTeX XMLCite \textit{K. M. Owolabi} and \textit{A. Atangana}, Chaos Solitons Fractals 105, 111--119 (2017; Zbl 1380.65120) Full Text: DOI
Liang, X.; Khaliq, A. Q. M.; Bhatt, H.; Furati, K. M. The locally extrapolated exponential splitting scheme for multi-dimensional nonlinear space-fractional Schrödinger equations. (English) Zbl 1380.65162 Numer. Algorithms 76, No. 4, 939-958 (2017). MSC: 65M06 65M12 65M15 35Q55 35R11 35Q51 PDFBibTeX XMLCite \textit{X. Liang} et al., Numer. Algorithms 76, No. 4, 939--958 (2017; Zbl 1380.65162) Full Text: DOI
Zeng, Fanhai; Li, Changpin A new Crank-Nicolson finite element method for the time-fractional subdiffusion equation. (English) Zbl 1372.65276 Appl. Numer. Math. 121, 82-95 (2017). MSC: 65M60 65M06 65M12 35K05 35R11 PDFBibTeX XMLCite \textit{F. Zeng} and \textit{C. Li}, Appl. Numer. Math. 121, 82--95 (2017; Zbl 1372.65276) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi An improved meshless method for solving two-dimensional distributed order time-fractional diffusion-wave equation with error estimate. (English) Zbl 1412.65131 Numer. Algorithms 75, No. 1, 173-211 (2017). MSC: 65M60 65M12 35R11 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Numer. Algorithms 75, No. 1, 173--211 (2017; Zbl 1412.65131) Full Text: DOI
Khaliq, A. Q. M.; Liang, X.; Furati, K. M. A fourth-order implicit-explicit scheme for the space fractional nonlinear Schrödinger equations. (English) Zbl 1365.65195 Numer. Algorithms 75, No. 1, 147-172 (2017). MSC: 65M06 35R11 35Q55 65M12 PDFBibTeX XMLCite \textit{A. Q. M. Khaliq} et al., Numer. Algorithms 75, No. 1, 147--172 (2017; Zbl 1365.65195) Full Text: DOI
Gao, Guang-hua; Sun, Zhi-zhong Two difference schemes for solving the one-dimensional time distributed-order fractional wave equations. (English) Zbl 1372.65229 Numer. Algorithms 74, No. 3, 675-697 (2017). Reviewer: Petr Sváček (Praha) MSC: 65M06 35L05 35R11 65M12 PDFBibTeX XMLCite \textit{G.-h. Gao} and \textit{Z.-z. Sun}, Numer. Algorithms 74, No. 3, 675--697 (2017; Zbl 1372.65229) Full Text: DOI
Du, Rui; Hao, Zhao-Peng; Sun, Zhi-Zhong Lubich second-order methods for distributed-order time-fractional differential equations with smooth solutions. (English) Zbl 1457.65047 East Asian J. Appl. Math. 6, No. 2, 131-151 (2016). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{R. Du} et al., East Asian J. Appl. Math. 6, No. 2, 131--151 (2016; Zbl 1457.65047) Full Text: DOI
Gao, Guang-hua; Sun, Zhi-zhong Two alternating direction implicit difference schemes for two-dimensional distributed-order fractional diffusion equations. (English) Zbl 1373.65055 J. Sci. Comput. 66, No. 3, 1281-1312 (2016). Reviewer: Charis Harley (Johannesburg) MSC: 65M06 35K05 35R11 65M12 PDFBibTeX XMLCite \textit{G.-h. Gao} and \textit{Z.-z. Sun}, J. Sci. Comput. 66, No. 3, 1281--1312 (2016; Zbl 1373.65055) Full Text: DOI
Li, Changpin; Yi, Qian; Chen, An Finite difference methods with non-uniform meshes for nonlinear fractional differential equations. (English) Zbl 1349.65246 J. Comput. Phys. 316, 614-631 (2016). MSC: 65L12 34A08 65L05 65L20 65L70 PDFBibTeX XMLCite \textit{C. Li} et al., J. Comput. Phys. 316, 614--631 (2016; Zbl 1349.65246) Full Text: DOI
Cao, Wanrong; Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em Implicit-explicit difference schemes for nonlinear fractional differential equations with nonsmooth solutions. (English) Zbl 1355.65104 SIAM J. Sci. Comput. 38, No. 5, A3070-A3093 (2016). MSC: 65L12 34A08 34A34 65L20 65L05 PDFBibTeX XMLCite \textit{W. Cao} et al., SIAM J. Sci. Comput. 38, No. 5, A3070--A3093 (2016; Zbl 1355.65104) Full Text: DOI arXiv
Doungmo Goufo, Emile Franc Stability and convergence analysis of a variable order replicator-mutator process in a moving medium. (English) Zbl 1343.92340 J. Theor. Biol. 403, 178-187 (2016). MSC: 92D15 92D25 91A22 PDFBibTeX XMLCite \textit{E. F. Doungmo Goufo}, J. Theor. Biol. 403, 178--187 (2016; Zbl 1343.92340) Full Text: DOI
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
Gao, Guang-Hua; Sun, Zhi-Zhong Two unconditionally stable and convergent difference schemes with the extrapolation method for the one-dimensional distributed-order differential equations. (English) Zbl 1339.65115 Numer. Methods Partial Differ. Equations 32, No. 2, 591-615 (2016). MSC: 65M06 65M12 PDFBibTeX XMLCite \textit{G.-H. Gao} and \textit{Z.-Z. Sun}, Numer. Methods Partial Differ. Equations 32, No. 2, 591--615 (2016; Zbl 1339.65115) Full Text: DOI
Li, Hefeng; Cao, Jianxiong; Li, Changpin High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations. III. (English) Zbl 1382.65251 J. Comput. Appl. Math. 299, 159-175 (2016). MSC: 65M06 65M12 26A33 35R11 PDFBibTeX XMLCite \textit{H. Li} et al., J. Comput. Appl. Math. 299, 159--175 (2016; Zbl 1382.65251) Full Text: DOI
Gao, Guang-hua; Sun, Zhi-zhong Two alternating direction implicit difference schemes with the extrapolation method for the two-dimensional distributed-order differential equations. (English) Zbl 1443.65124 Comput. Math. Appl. 69, No. 9, 926-948 (2015). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{G.-h. Gao} and \textit{Z.-z. Sun}, Comput. Math. Appl. 69, No. 9, 926--948 (2015; Zbl 1443.65124) Full Text: DOI
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
Gao, Guang-hua; Sun, Hai-wei; Sun, Zhi-zhong Some high-order difference schemes for the distributed-order differential equations. (English) Zbl 1349.65296 J. Comput. Phys. 298, 337-359 (2015). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{G.-h. Gao} et al., J. Comput. Phys. 298, 337--359 (2015; Zbl 1349.65296) Full Text: DOI
Ding, Hengfei; Li, Changpin; Chen, YangQuan High-order algorithms for Riesz derivative and their applications. II. (English) Zbl 1349.65284 J. Comput. Phys. 293, 218-237 (2015). MSC: 65M06 35R11 65D25 65M12 PDFBibTeX XMLCite \textit{H. Ding} et al., J. Comput. Phys. 293, 218--237 (2015; Zbl 1349.65284) Full Text: DOI
Atangana, Abdon On the stability and convergence of the time-fractional variable order telegraph equation. (English) Zbl 1349.65263 J. Comput. Phys. 293, 104-114 (2015). MSC: 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{A. Atangana}, J. Comput. Phys. 293, 104--114 (2015; Zbl 1349.65263) Full Text: DOI
Jin, Bangti; Lazarov, Raytcho; Pasciak, Joseph; Rundell, William Variational formulation of problems involving fractional order differential operators. (English) Zbl 1321.65127 Math. Comput. 84, No. 296, 2665-2700 (2015). MSC: 65L60 34A08 34B15 65L10 65L20 65L70 34L16 PDFBibTeX XMLCite \textit{B. Jin} et al., Math. Comput. 84, No. 296, 2665--2700 (2015; Zbl 1321.65127) Full Text: DOI arXiv
Wu, Shu-Lin; Zhou, Tao Convergence analysis for three parareal solvers. (English) Zbl 1328.65157 SIAM J. Sci. Comput. 37, No. 2, A970-A992 (2015). MSC: 65L05 65L20 68Q60 PDFBibTeX XMLCite \textit{S.-L. Wu} and \textit{T. Zhou}, SIAM J. Sci. Comput. 37, No. 2, A970--A992 (2015; Zbl 1328.65157) Full Text: DOI
Cao, Jianxiong; Li, Changpin; Chen, YangQuan High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations. II. (English) Zbl 1325.65121 Fract. Calc. Appl. Anal. 18, No. 3, 735-761 (2015). MSC: 65M06 65M12 26A33 PDFBibTeX XMLCite \textit{J. Cao} et al., Fract. Calc. Appl. Anal. 18, No. 3, 735--761 (2015; Zbl 1325.65121) Full Text: DOI
Mao, Zhi; Xiao, Aiguo; Yu, Zuguo; Shi, Long Finite difference and sinc-collocation approximations to a class of fractional diffusion-wave equations. (English) Zbl 1442.65295 J. Appl. Math. 2014, Article ID 536030, 11 p. (2014). MSC: 65M70 35R11 65M06 65M12 PDFBibTeX XMLCite \textit{Z. Mao} et al., J. Appl. Math. 2014, Article ID 536030, 11 p. (2014; Zbl 1442.65295) Full Text: DOI
Zhang, Yuxin; Ding, Hengfei; Luo, Jincai Fourth-order compact difference schemes for the Riemann-Liouville and Riesz derivatives. (English) Zbl 1468.65022 Abstr. Appl. Anal. 2014, Article ID 540692, 4 p. (2014). MSC: 65D25 26A33 PDFBibTeX XMLCite \textit{Y. Zhang} et al., Abstr. Appl. Anal. 2014, Article ID 540692, 4 p. (2014; Zbl 1468.65022) Full Text: DOI
Vong, Seakweng; Wang, Zhibo A compact difference scheme for a two dimensional fractional Klein-Gordon equation with Neumann boundary conditions. (English) Zbl 1352.65273 J. Comput. Phys. 274, 268-282 (2014). MSC: 65M06 35R11 35L20 39A14 65M12 PDFBibTeX XMLCite \textit{S. Vong} and \textit{Z. Wang}, J. Comput. Phys. 274, 268--282 (2014; Zbl 1352.65273) Full Text: DOI
Atangana, Abdon On the solution of an acoustic wave equation with variable-order derivative loss operator. (English) Zbl 1444.65047 Adv. Difference Equ. 2013, Paper No. 167, 12 p. (2013). MSC: 65M06 35L05 35R11 26A33 PDFBibTeX XMLCite \textit{A. Atangana}, Adv. Difference Equ. 2013, Paper No. 167, 12 p. (2013; Zbl 1444.65047) Full Text: DOI
Atangana, Abdon; Oukouomi Noutchie, S. C. Stability and convergence of a time-fractional variable order Hantush equation for a deformable aquifer. (English) Zbl 1301.76072 Abstr. Appl. Anal. 2013, Article ID 691060, 8 p. (2013). MSC: 76S05 35B35 35R11 65M06 65M12 86A05 PDFBibTeX XMLCite \textit{A. Atangana} and \textit{S. C. Oukouomi Noutchie}, Abstr. Appl. Anal. 2013, Article ID 691060, 8 p. (2013; Zbl 1301.76072) Full Text: DOI
Cui, Mingrong Convergence analysis of high-order compact alternating direction implicit schemes for the two-dimensional time fractional diffusion equation. (English) Zbl 1264.65143 Numer. Algorithms 62, No. 3, 383-409 (2013). Reviewer: Rémi Vaillancourt (Ottawa) MSC: 65M12 65M06 35K20 35R11 PDFBibTeX XMLCite \textit{M. Cui}, Numer. Algorithms 62, No. 3, 383--409 (2013; Zbl 1264.65143) Full Text: DOI
Alikhanov, Anatoly A. Boundary value problems for the diffusion equation of the variable order in differential and difference settings. (English) Zbl 1311.35332 Appl. Math. Comput. 219, No. 8, 3938-3946 (2012). MSC: 35R11 35B45 PDFBibTeX XMLCite \textit{A. A. Alikhanov}, Appl. Math. Comput. 219, No. 8, 3938--3946 (2012; Zbl 1311.35332) Full Text: DOI arXiv
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
Li, Can; Deng, Weihua; Wu, Yujiang Finite difference approximations and dynamics simulations for the Lévy fractional Klein-Kramers equation. (English) Zbl 1312.65137 Numer. Methods Partial Differ. Equations 28, No. 6, 1944-1965 (2012). MSC: 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{C. Li} et al., Numer. Methods Partial Differ. Equations 28, No. 6, 1944--1965 (2012; Zbl 1312.65137) Full Text: DOI
Cui, Mingrong Compact alternating direction implicit method for two-dimensional time fractional diffusion equation. (English) Zbl 1242.65158 J. Comput. Phys. 231, No. 6, 2621-2633 (2012). MSC: 65M06 35K05 35R11 65M12 65M15 PDFBibTeX XMLCite \textit{M. Cui}, J. Comput. Phys. 231, No. 6, 2621--2633 (2012; Zbl 1242.65158) Full Text: DOI
Quintana-Murillo, J.; Yuste, S. B. An explicit numerical method for the fractional cable equation. (English) Zbl 1237.65097 Int. J. Differ. Equ. 2011, Article ID 231920, 12 p. (2011). MSC: 65M06 35L10 35R11 65M12 PDFBibTeX XMLCite \textit{J. Quintana-Murillo} and \textit{S. B. Yuste}, Int. J. Differ. Equ. 2011, Article ID 231920, 12 p. (2011; Zbl 1237.65097) Full Text: DOI
Scherer, Rudolf; Kalla, Shyam L.; Tang, Yifa; Huang, Jianfei The Grünwald-Letnikov method for fractional differential equations. (English) Zbl 1228.65121 Comput. Math. Appl. 62, No. 3, 902-917 (2011). MSC: 65L12 34A08 26A33 45J05 65L20 PDFBibTeX XMLCite \textit{R. Scherer} et al., Comput. Math. Appl. 62, No. 3, 902--917 (2011; Zbl 1228.65121) Full Text: DOI
Su, Lijuan; Wang, Wenqia; Wang, Hong A characteristic difference method for the transient fractional convection-diffusion equations. (English) Zbl 1225.65085 Appl. Numer. Math. 61, No. 8, 946-960 (2011). Reviewer: Jialin Hong (Beijing) MSC: 65M06 35K20 35R11 65M12 65M25 PDFBibTeX XMLCite \textit{L. Su} et al., Appl. Numer. Math. 61, No. 8, 946--960 (2011; Zbl 1225.65085) Full Text: DOI
Li, Changpin; Chen, An; Ye, Junjie Numerical approaches to fractional calculus and fractional ordinary differential equation. (English) Zbl 1218.65070 J. Comput. Phys. 230, No. 9, 3352-3368 (2011). MSC: 65L05 34A08 34A34 65L20 65L70 PDFBibTeX XMLCite \textit{C. Li} et al., J. Comput. Phys. 230, No. 9, 3352--3368 (2011; Zbl 1218.65070) Full Text: DOI
Gao, Guanghua; Sun, Zhizhong A compact finite difference scheme for the fractional sub-diffusion equations. (English) Zbl 1211.65112 J. Comput. Phys. 230, No. 3, 586-595 (2011). Reviewer: Damian Słota (Gliwice) MSC: 65M06 35K05 35R11 65M12 PDFBibTeX XMLCite \textit{G. Gao} and \textit{Z. Sun}, J. Comput. Phys. 230, No. 3, 586--595 (2011; Zbl 1211.65112) Full Text: DOI
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
Cui, Mingrong Compact finite difference method for the fractional diffusion equation. (English) Zbl 1179.65107 J. Comput. Phys. 228, No. 20, 7792-7804 (2009). Reviewer: Ivan Secrieru (Chişinău) MSC: 65M06 65M12 35R11 35K05 65M15 PDFBibTeX XMLCite \textit{M. Cui}, J. Comput. Phys. 228, No. 20, 7792--7804 (2009; Zbl 1179.65107) Full Text: DOI