Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

Efficient and Accurate Spectral Method for Solving Fractional Differential Equations on the Half Line Using Orthogonal Generalized Rational Jacobi Functions

Tarek Aboelenen
Communications on Applied Mathematics and Computation (2024)
https://doi.org/10.1007/s42967-023-00337-y

Stability and Time-Step Constraints of Implicit-Explicit Runge-Kutta Methods for the Linearized Korteweg-de Vries Equation

Joseph Hunter, Zheng Sun and Yulong Xing
Communications on Applied Mathematics and Computation 6 (1) 658 (2024)
https://doi.org/10.1007/s42967-023-00285-7

Computational study based on the Laplace transform and local discontinuous Galerkin methods for solving fourth-order time-fractional partial integro-differential equations with weakly singular kernels

Hadi Mohammadi-Firouzjaei, Hojatollah Adibi and Mehdi Dehghan
Computational and Applied Mathematics 43 (6) (2024)
https://doi.org/10.1007/s40314-024-02813-4

Modelling Fractional Advection–Diffusion Processes via the Adomian Decomposition

Alberto Antonini and Valentina Anna Lia Salomoni
Mathematics 11 (12) 2657 (2023)
https://doi.org/10.3390/math11122657

An efficient compact difference-proper orthogonal decomposition algorithm for fractional viscoelastic plate vibration model

Qing Li and Huanzhen Chen
Computers & Mathematics with Applications 151 190 (2023)
https://doi.org/10.1016/j.camwa.2023.09.024

The solution of the time-space fractional diffusion equation based on the Chebyshev collocation method

Junsheng Duan and Lixia Jing
Indian Journal of Pure and Applied Mathematics (2023)
https://doi.org/10.1007/s13226-023-00495-y

Hybridizable discontinuous Galerkin methods for space-time fractional advection-dispersion equations

Jingjun Zhao, Wenjiao Zhao and Yang Xu
Applied Mathematics and Computation 442 127745 (2023)
https://doi.org/10.1016/j.amc.2022.127745

Local discontinuous Galerkin method for the Riesz space distributed-order Sobolev equation

Somayeh Fouladi and Hadi Mohammadi-Firouzjaei
Engineering Analysis with Boundary Elements 155 38 (2023)
https://doi.org/10.1016/j.enganabound.2023.05.046

A direct discontinuous Galerkin method for a high order nonlocal conservation law

Afaf Bouharguane and Nour Seloula
Computers & Mathematics with Applications 141 1 (2023)
https://doi.org/10.1016/j.camwa.2023.03.022

Stability analysis and error estimates of local discontinuous Galerkin method for nonlinear fractional Ginzburg–Landau equation with the fractional Laplacian

Tarek Aboelenen and Mohammed Alqawba
The European Physical Journal Special Topics 232 (14-15) 2607 (2023)
https://doi.org/10.1140/epjs/s11734-023-00921-6

Local discontinuous Galerkin schemes for an ultrasonic propagation equation with fractional attenuation

Can Li, Min-Min Li and Zine El Abiddine Fellah
Discrete and Continuous Dynamical Systems - B 28 (11) 5494 (2023)
https://doi.org/10.3934/dcdsb.2023063

Stability analysis and error estimates of implicit Runge-Kutta local discontinuous Galerkin methods for linear bi-harmonic equation

Hui Bi and Mengyuan Zhang
Computers & Mathematics with Applications 149 211 (2023)
https://doi.org/10.1016/j.camwa.2023.09.022

Numerical analysis for compact difference scheme of fractional viscoelastic beam vibration models

Qing Li and Huanzhen Chen
Applied Mathematics and Computation 427 127146 (2022)
https://doi.org/10.1016/j.amc.2022.127146

LDG approximation of a nonlinear fractional convection-diffusion equation using B-spline basis functions

Hamid Safdari, Majid Rajabzadeh and Moein Khalighi
Applied Numerical Mathematics 171 45 (2022)
https://doi.org/10.1016/j.apnum.2021.08.014

Time two-grid technique combined with temporal second order difference method for two-dimensional semilinear fractional sub-diffusion equations

Dakang Cen and Zhibo Wang
Applied Mathematics Letters 129 107919 (2022)
https://doi.org/10.1016/j.aml.2022.107919

Computing solution landscape of nonlinear space-fractional problems via fast approximation algorithm

Bing Yu, Xiangcheng Zheng, Pingwen Zhang and Lei Zhang
Journal of Computational Physics 468 111513 (2022)
https://doi.org/10.1016/j.jcp.2022.111513

Local discontinuous Galerkin method based on a family of second-order time approximation schemes for fractional mobile/immobile convection-diffusion equations

Yuxuan Niu, Jinfeng Wang, Yang Liu, Hong Li and Zhichao Fang
Applied Numerical Mathematics 179 149 (2022)
https://doi.org/10.1016/j.apnum.2022.04.020

Stability analysis and error estimates of implicit–explicit Runge–Kutta local discontinuous Galerkin methods for nonlinear fractional convection–diffusion problems

Tarek Aboelenen
Computational and Applied Mathematics 41 (6) (2022)
https://doi.org/10.1007/s40314-022-01954-8

Convergence Analysis of a LDG Method for Time–Space Tempered Fractional Diffusion Equations with Weakly Singular Solutions

Z. Safari, G. B. Loghmani and M. Ahmadinia
Journal of Scientific Computing 91 (2) (2022)
https://doi.org/10.1007/s10915-022-01835-6

A fast numerical scheme for a variably distributed-order time-fractional diffusion equation and its analysis

Jinhong Jia, Hong Wang and Xiangcheng Zheng
Computers & Mathematics with Applications 108 24 (2022)
https://doi.org/10.1016/j.camwa.2021.12.016

Probability-conservative simulation for Lévy financial model by a mixed finite element method

Jing Chen, Feng Wang and Huanzhen Chen
Computers & Mathematics with Applications 106 92 (2022)
https://doi.org/10.1016/j.camwa.2021.12.007

Discretization and Analysis of an Optimal Control of a Variable-Order Time-Fractional Diffusion Equation with Pointwise Constraints

Xiangcheng Zheng and Hong Wang
Journal of Scientific Computing 91 (2) (2022)
https://doi.org/10.1007/s10915-022-01795-x

Local Discontinuous Galerkin Methods with Novel Basis for Fractional Diffusion Equations with Non-smooth Solutions

Liyao Lyu and Zheng Chen
Communications on Applied Mathematics and Computation 4 (1) 227 (2022)
https://doi.org/10.1007/s42967-020-00104-3

Fully spectral‐Galerkin method for the one‐ and two‐dimensional fourth‐order time‐fractional partial integro‐differential equations with a weakly singular kernel

Farhad Fakhar‐Izadi
Numerical Methods for Partial Differential Equations 38 (2) 160 (2022)
https://doi.org/10.1002/num.22634

The Crank‐Nicolson/interpolating stabilized element‐free Galerkin method to investigate the fractional Galilei invariant advection‐diffusion equation

Mostafa Abbaszadeh and Mehdi Dehghan
Mathematical Methods in the Applied Sciences 44 (4) 2752 (2021)
https://doi.org/10.1002/mma.5871

Lagrange nodal discontinuous Galerkin method for fractional Navier-Stokes equations

Jingjun Zhao, Wenjiao Zhao and Yang Xu
Applied Mathematics and Computation 391 125697 (2021)
https://doi.org/10.1016/j.amc.2020.125697

Local discontinuous Galerkin method for the fractional diffusion equation with integral fractional Laplacian

Daxin Nie and Weihua Deng
Computers & Mathematics with Applications 104 44 (2021)
https://doi.org/10.1016/j.camwa.2021.11.007

A CG–DG method for Maxwell’s equations in Cole–Cole dispersive media

Jiangxing Wang, Jiwei Zhang and Zhimin Zhang
Journal of Computational and Applied Mathematics 393 113480 (2021)
https://doi.org/10.1016/j.cam.2021.113480

A characteristic finite element method for the time-fractional mobile/immobile advection diffusion model

Huan Liu, Xiangcheng Zheng, Chuanjun Chen and Hong Wang
Advances in Computational Mathematics 47 (3) (2021)
https://doi.org/10.1007/s10444-021-09867-6

Local discontinuous Galerkin method for a nonlocal viscous conservation laws

Can Li and Shuming Liu
International Journal for Numerical Methods in Fluids 93 (1) 197 (2021)
https://doi.org/10.1002/fld.4880

On circulant and skew-circulant preconditioned Krylov methods for steady-state Riesz spatial fractional diffusion equations

Mu-Zheng Zhu, Ya-E Qi and Guo-Feng Zhang
Linear and Multilinear Algebra 69 (4) 719 (2021)
https://doi.org/10.1080/03081087.2019.1617230

Solvability and approximation of two-side conservative fractional diffusion problems with variable-Coefficient based on least-Squares

Suxiang Yang, Huanzhen Chen, Vincent J. Ervin and Hong Wang
Applied Mathematics and Computation 406 126229 (2021)
https://doi.org/10.1016/j.amc.2021.126229

Two-grid methods for nonlinear time fractional diffusion equations by L1-Galerkin FEM

Qingfeng Li, Yanping Chen, Yunqing Huang and Yang Wang
Mathematics and Computers in Simulation 185 436 (2021)
https://doi.org/10.1016/j.matcom.2020.12.033

Error Estimate of a Fully Discrete Local Discontinuous Galerkin Method for Variable-Order Time-Fractional Diffusion Equations

Leilei Wei, Shuying Zhai and Xindong Zhang
Communications on Applied Mathematics and Computation 3 (3) 429 (2021)
https://doi.org/10.1007/s42967-020-00081-7

Solving a non-linear fractional convection-diffusion equation using local discontinuous Galerkin method

Hamid Safdari, Majid Rajabzadeh and Moein Khalighi
Applied Numerical Mathematics 165 22 (2021)
https://doi.org/10.1016/j.apnum.2021.02.003

Non-uniform L1/discontinuous Galerkin approximation for the time-fractional convection equation with weak regular solution

Changpin Li and Zhen Wang
Mathematics and Computers in Simulation 182 838 (2021)
https://doi.org/10.1016/j.matcom.2020.12.007

Bayesian calibration of order and diffusivity parameters in a fractional diffusion equation

Hasnaa H Alzahrani, Marco Lucchesi, Kassem Mustapha, Olivier P Le Maître and Omar M Knio
Journal of Physics Communications 5 (8) 085014 (2021)
https://doi.org/10.1088/2399-6528/ac1507

Local discontinuous Galerkin method for distributed‐order time‐fractional diffusion‐wave equation: Application of Laplace transform

Hadi Mohammadi‐Firouzjaei, Hojatollah Adibi and Mehdi Dehghan
Mathematical Methods in the Applied Sciences 44 (6) 4923 (2021)
https://doi.org/10.1002/mma.7077

Convergence analysis of a LDG method for tempered fractional convection–diffusion equations

Mahdi Ahmadinia and Zeinab Safari
ESAIM: Mathematical Modelling and Numerical Analysis 54 (1) 59 (2020)
https://doi.org/10.1051/m2an/2019052

High-Order Local Discontinuous Galerkin Algorithm with Time Second-Order Schemes for the Two-Dimensional Nonlinear Fractional Diffusion Equation

Min Zhang, Yang Liu and Hong Li
Communications on Applied Mathematics and Computation 2 (4) 613 (2020)
https://doi.org/10.1007/s42967-019-00058-1

Finite element methods for fractional diffusion equations

Yue Zhao, Chen Shen, Min Qu, Weiping Bu and Yifa Tang
International Journal of Modeling, Simulation, and Scientific Computing 11 (04) 2030001 (2020)
https://doi.org/10.1142/S1793962320300010

Particle simulation of space–fractional diffusion equations

M. Lucchesi, S. Allouch, O. P. Le Maître, K. A. Mustapha and O. M. Knio
Computational Particle Mechanics 7 (3) 491 (2020)
https://doi.org/10.1007/s40571-019-00275-8

Local Discontinuous Galerkin Scheme for Space Fractional Allen–Cahn Equation

Can Li and Shuming Liu
Communications on Applied Mathematics and Computation 2 (1) 73 (2020)
https://doi.org/10.1007/s42967-019-00034-9

Local discontinuous Galerkin method for time variable order fractional differential equations with sub-diffusion and super-diffusion

M. Ahmadinia, Z. Safari and M. Abbasi
Applied Numerical Mathematics 157 602 (2020)
https://doi.org/10.1016/j.apnum.2020.07.015

On the Convergence of the Local Discontinuous Galerkin Method Applied to a Stationary One Dimensional Fractional Diffusion Problem

P. Castillo and S. Gómez
Journal of Scientific Computing 85 (2) (2020)
https://doi.org/10.1007/s10915-020-01335-5

On group analysis of the time fractional extended (2+1)-dimensional Zakharov–Kuznetsov equation in quantum magneto-plasmas

Jian-Gen Liu, Xiao-Jun Yang, Yi-Ying Feng and Ping Cui
Mathematics and Computers in Simulation 178 407 (2020)
https://doi.org/10.1016/j.matcom.2020.07.005

A time two-grid algorithm based on finite difference method for the two-dimensional nonlinear time-fractional mobile/immobile transport model

Wenlin Qiu, Da Xu, Jing Guo and Jun Zhou
Numerical Algorithms 85 (1) 39 (2020)
https://doi.org/10.1007/s11075-019-00801-y

Direct meshless local Petrov–Galerkin (DMLPG) method for time-fractional fourth-order reaction–diffusion problem on complex domains

Mostafa Abbaszadeh and Mehdi Dehghan
Computers & Mathematics with Applications 79 (3) 876 (2020)
https://doi.org/10.1016/j.camwa.2019.08.001

A Finite Difference Method for Space Fractional Differential Equations with Variable Diffusivity Coefficient

K. A. Mustapha, K. M. Furati, O. M. Knio and O. P. Le Maître
Communications on Applied Mathematics and Computation 2 (4) 671 (2020)
https://doi.org/10.1007/s42967-020-00066-6

A High Order Formula to Approximate the Caputo Fractional Derivative

R. Mokhtari and F. Mostajeran
Communications on Applied Mathematics and Computation 2 (1) 1 (2020)
https://doi.org/10.1007/s42967-019-00023-y

The local discontinuous Galerkin method for convection-diffusion-fractional anti-diffusion equations

Afaf Bouharguane and Nour Seloula
Applied Numerical Mathematics 148 61 (2020)
https://doi.org/10.1016/j.apnum.2019.09.001

Numerical algorithm for the model describing anomalous diffusion in expanding media

Daxin Nie, Jing Sun and Weihua Deng
ESAIM: Mathematical Modelling and Numerical Analysis 54 (6) 2265 (2020)
https://doi.org/10.1051/m2an/2020018

Hierarchical matrix approximations for space-fractional diffusion equations

Wajih Boukaram, Marco Lucchesi, George Turkiyyah, et al.
Computer Methods in Applied Mechanics and Engineering 369 113191 (2020)
https://doi.org/10.1016/j.cma.2020.113191

Local discontinuous Galerkin methods for the time tempered fractional diffusion equation

Xiaorui Sun, Can Li and Fengqun Zhao
Applied Mathematics and Computation 365 124725 (2020)
https://doi.org/10.1016/j.amc.2019.124725

A two-grid MMOC finite element method for nonlinear variable-order time-fractional mobile/immobile advection–diffusion equations

Chuanjun Chen, Huan Liu, Xiangcheng Zheng and Hong Wang
Computers & Mathematics with Applications 79 (9) 2771 (2020)
https://doi.org/10.1016/j.camwa.2019.12.008

A Local Discontinuous Galerkin Method for Two-Dimensional Time Fractional Diffusion Equations

Somayeh Yeganeh, Reza Mokhtari and Jan S. Hesthaven
Communications on Applied Mathematics and Computation 2 (4) 689 (2020)
https://doi.org/10.1007/s42967-020-00065-7

A fast second‐order difference scheme for the space–time fractional equation

Weiyan Xu and Hong Sun
Numerical Methods for Partial Differential Equations 35 (4) 1326 (2019)
https://doi.org/10.1002/num.22352

Fast finite difference methods for space-time fractional partial differential equations in three space dimensions with nonlocal boundary conditions

Meng Zhao and Hong Wang
Applied Numerical Mathematics 145 411 (2019)
https://doi.org/10.1016/j.apnum.2019.05.007

Optimal stabilization and time step constraints for the forward Euler-Local Discontinuous Galerkin method applied to fractional diffusion equations

Paul Castillo and Sergio Gómez
Journal of Computational Physics 394 503 (2019)
https://doi.org/10.1016/j.jcp.2019.06.005

The time-fractional diffusion inverse problem subject to an extra measurement by a local discontinuous Galerkin method

Samaneh Qasemi, Davood Rostamy and Nazdar Abdollahi
BIT Numerical Mathematics 59 (1) 183 (2019)
https://doi.org/10.1007/s10543-018-0731-z

On single-step HSS iterative method with circulant preconditioner for fractional diffusion equations

Mu-Zheng Zhu, Guo-Feng Zhang and Ya-E Qi
Advances in Difference Equations 2019 (1) (2019)
https://doi.org/10.1186/s13662-019-2353-4

LDG schemes with second order implicit time discretization for a fractional sub-diffusion equation

Can Li, Xiaorui Sun and Fengqun Zhao
Results in Applied Mathematics 4 100079 (2019)
https://doi.org/10.1016/j.rinam.2019.100079

Central local discontinuous Galerkin method for the space fractional diffusion equation

Jing Sun, Daxin Nie and Weihua Deng
Computers & Mathematics with Applications 78 (5) 1274 (2019)
https://doi.org/10.1016/j.camwa.2019.02.002

Quenching study of two-dimensional fractional reaction–diffusion equation from combustion process

Qinwu Xu and Yufeng Xu
Computers & Mathematics with Applications 78 (5) 1490 (2019)
https://doi.org/10.1016/j.camwa.2019.04.006

Least‐squares mixed Galerkin formulation for variable‐coefficient fractional differential equations with D‐N boundary condition

Feng Wang, Huanzhen Chen and Hong Wang
Mathematical Methods in the Applied Sciences 42 (12) 4331 (2019)
https://doi.org/10.1002/mma.5653

Numerical Methods for Solving Space Fractional Partial Differential Equations Using Hadamard Finite-Part Integral Approach

Yanyong Wang, Yubin Yan and Ye Hu
Communications on Applied Mathematics and Computation 1 (4) 505 (2019)
https://doi.org/10.1007/s42967-019-00036-7

A fast finite volume method for conservative space–time fractional diffusion equations discretized on space–time locally refined meshes

Jinhong Jia and Hong Wang
Computers & Mathematics with Applications 78 (5) 1345 (2019)
https://doi.org/10.1016/j.camwa.2019.04.003

Least-Squared Mixed Variational Formulation Based on Space Decomposition for a Kind of Variable-Coefficient Fractional Diffusion Problems

Suxiang Yang, Huanzhen Chen and Hong Wang
Journal of Scientific Computing 78 (2) 687 (2019)
https://doi.org/10.1007/s10915-018-0782-y

Analysis of mixed finite element method (MFEM) for solving the generalized fractional reaction–diffusion equation on nonrectangular domains

Mostafa Abbaszadeh and Mehdi Dehghan
Computers & Mathematics with Applications 78 (5) 1531 (2019)
https://doi.org/10.1016/j.camwa.2019.03.040

Optimal convergence rates for semidiscrete finite element approximations of linear space-fractional partial differential equations under minimal regularity assumptions

Fang Liu, Zongqi Liang and Yubin Yan
Journal of Computational and Applied Mathematics 352 409 (2019)
https://doi.org/10.1016/j.cam.2018.12.004

Variational formulation and efficient implementation for solving the tempered fractional problems

Weihua Deng and Zhijiang Zhang
Numerical Methods for Partial Differential Equations 34 (4) 1224 (2018)
https://doi.org/10.1002/num.22254

On the Conservation of Fractional Nonlinear Schrödinger Equation’s Invariants by the Local Discontinuous Galerkin Method

P. Castillo and S. Gómez
Journal of Scientific Computing 77 (3) 1444 (2018)
https://doi.org/10.1007/s10915-018-0708-8

Analysis of local discontinuous Galerkin method for time–space fractional convection–diffusion equations

M. Ahmadinia, Z. Safari and S. Fouladi
BIT Numerical Mathematics 58 (3) 533 (2018)
https://doi.org/10.1007/s10543-018-0697-x

Local discontinuous Galerkin method for distributed-order time and space-fractional convection–diffusion and Schrödinger-type equations

Tarek Aboelenen
Nonlinear Dynamics 92 (2) 395 (2018)
https://doi.org/10.1007/s11071-018-4063-y

A direct discontinuous Galerkin method for fractional convection-diffusion and Schrödinger-type equations

Tarek Aboelenen
The European Physical Journal Plus 133 (8) (2018)
https://doi.org/10.1140/epjp/i2018-12166-y

An expanded mixed finite element simulation for two-sided time-dependent fractional diffusion problem

Qiong Yuan and Huanzhen Chen
Advances in Difference Equations 2018 (1) (2018)
https://doi.org/10.1186/s13662-018-1483-4

Extremely low order time-fractional differential equation and application in combustion process

Qinwu Xu and Yufeng Xu
Communications in Nonlinear Science and Numerical Simulation 64 135 (2018)
https://doi.org/10.1016/j.cnsns.2018.04.021

ADI Galerkin FEMs for the 2D nonlinear time-space fractional diffusion-wave equation

Meng Li and Chengming Huang
International Journal of Modeling, Simulation, and Scientific Computing 08 (03) 1750025 (2017)
https://doi.org/10.1142/S1793962317500258

Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion Equations

Meilan Qiu, Liquan Mei and Dewang Li
Advances in Mathematical Physics 2017 1 (2017)
https://doi.org/10.1155/2017/4961797

Mixed-Type Galerkin Variational Principle and Numerical Simulation for a Generalized Nonlocal Elastic Model

Lueling Jia, Huanzhen Chen and Hong Wang
Journal of Scientific Computing 71 (2) 660 (2017)
https://doi.org/10.1007/s10915-016-0316-4

Solution of two-dimensional time-fractional Burgers equation with high and low Reynolds numbers

Wen Cao, Qinwu Xu and Zhoushun Zheng
Advances in Difference Equations 2017 (1) (2017)
https://doi.org/10.1186/s13662-017-1398-5

A mixed‐type Galerkin variational formulation and fast algorithms for variable‐coefficient fractional diffusion equations

Yongshan Li, Huanzhen Chen and Hong Wang
Mathematical Methods in the Applied Sciences 40 (14) 5018 (2017)
https://doi.org/10.1002/mma.4367

Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains

Z. Yang, Z. Yuan, Y. Nie, et al.
Journal of Computational Physics 330 863 (2017)
https://doi.org/10.1016/j.jcp.2016.10.053

Discontinuous Galerkin time stepping method for solving linear space fractional partial differential equations

Yanmei Liu, Yubin Yan and Monzorul Khan
Applied Numerical Mathematics 115 200 (2017)
https://doi.org/10.1016/j.apnum.2017.01.009

A Petrov–Galerkin spectral element method for fractional elliptic problems

Ehsan Kharazmi, Mohsen Zayernouri and George Em Karniadakis
Computer Methods in Applied Mechanics and Engineering 324 512 (2017)
https://doi.org/10.1016/j.cma.2017.06.006

Schwartz duality of the Dirac delta function for the Chebyshev collocation approximation to the fractional advection equation

He Yang, Jingyang Guo and Jae-Hun Jung
Applied Mathematics Letters 64 205 (2017)
https://doi.org/10.1016/j.aml.2016.09.009

Fractional Burgers equation with nonlinear non-locality: Spectral vanishing viscosity and local discontinuous Galerkin methods

Zhiping Mao and George Em Karniadakis
Journal of Computational Physics 336 143 (2017)
https://doi.org/10.1016/j.jcp.2017.01.048