A novel spectral Galerkin/Petrov–Galerkin algorithm for the multi-dimensional space–time fractional advection–diffusion–reaction equations with nonsmooth solutions

A class of efficient time-stepping methods for multi-term time-fractional reaction-diffusion-wave equations

(2021) Baoli Yin et al.   APPLIED NUMERICAL MATHEMATICS

Optimal Regularity and Error Estimates of a Spectral Galerkin Method for Fractional Advection-Diffusion-Reaction Equations

(2020) Zhaopeng Hao et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Necessity of introducing non-integer shifted parameters by constructing high accuracy finite difference algorithms for a two-sided space-fractional advection–diffusion model

(2020) Baoli Yin et al.   APPLIED MATHEMATICS LETTERS

Mass- and energy-conserving difference schemes for nonlinear fractional Schrödinger equations

(2020) Xiaoxi Li et al.   APPLIED MATHEMATICS LETTERS

A structure preserving difference scheme with fast algorithms for high dimensional nonlinear space-fractional Schrödinger equations

(2020) Baoli Yin et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Optimal-order finite element approximations to variable-coefficient two-sided space-fractional advection-reaction-diffusion equations in three space dimensions

(2020) Xiangcheng Zheng et al.   APPLIED NUMERICAL MATHEMATICS

Existence, uniqueness and numerical analysis of solutions of tempered fractional boundary value problems

(2019) Mahmoud A. Zaky   APPLIED NUMERICAL MATHEMATICS

Multi-dimensional spectral tau methods for distributed-order fractional diffusion equations

(2019) Mahmoud A. Zaky et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Optimal error estimates for Chebyshev approximations of functions with limited regularity in fractional Sobolev-type spaces

(2019) Wenjie Liu et al.   MATHEMATICS OF COMPUTATION

Recovery of high order accuracy in Jacobi spectral collocation methods for fractional terminal value problems with non-smooth solutions

(2019) Mahmoud A. Zaky   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Analysis of Spectral Approximations Using Eigenfunctions of Fractional Sturm–Liouville Problems

(2019) Haiyong Wang   JOURNAL OF SCIENTIFIC COMPUTING

An Efficient Space–Time Method for Time Fractional Diffusion Equation

(2019) Jie Shen et al.   JOURNAL OF SCIENTIFIC COMPUTING

Long time numerical behaviors of fractional pantograph equations

(2019) Dongfang Li et al.   MATHEMATICS AND COMPUTERS IN SIMULATION

A spectral framework for fractional variational problems based on fractional Jacobi functions

(2018) M.A. Zaky et al.   APPLIED NUMERICAL MATHEMATICS

A unified spectral method for FPDEs with two-sided derivatives; Part II: Stability, and error analysis

(2018) Mehdi Samiee et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Enriched Spectral Methods and Applications to Problems with Weakly Singular Solutions

(2018) Sheng Chen et al.   JOURNAL OF SCIENTIFIC COMPUTING

Regularity theory and high order numerical methods for the (1D)-fractional Laplacian

(2017) Gabriel Acosta et al.   MATHEMATICS OF COMPUTATION

Unconditionally Convergent $L1$-Galerkin FEMs for Nonlinear Time-Fractional Schrödinger Equations

(2017) Dongfang Li et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Shifted fractional-order Jacobi orthogonal functions: Application to a system of fractional differential equations

(2016) A.H. Bhrawy et al.   APPLIED MATHEMATICAL MODELLING

The use of element free Galerkin method based on moving Kriging and radial point interpolation techniques for solving some types of Turing models

(2016) Mehdi Dehghan et al.   ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS

Analysis of two methods based on Galerkin weak form for fractional diffusion-wave: Meshless interpolating element free Galerkin (IEFG) and finite element methods

(2016) Mehdi Dehghan et al.   ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS

On the Optimal Estimates and Comparison of Gegenbauer Expansion Coefficients

(2016) Haiyong Wang   SIAM JOURNAL ON NUMERICAL ANALYSIS

Polynomial spectral collocation method for space fractional advection-diffusion equation

(2014) WenYi Tian et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Fractional Sturm–Liouville eigen-problems: Theory and numerical approximation

(2013) Mohsen Zayernouri et al.   JOURNAL OF COMPUTATIONAL PHYSICS