A fast collocation approximation to a two-sided variable-order space-fractional diffusion equation and its analysis

A fast method for variable-order space-fractional diffusion equations

(2020) Jinhong Jia et al.   NUMERICAL ALGORITHMS

An Optimal-Order Numerical Approximation to Variable-order Space-fractional Diffusion Equations on Uniform or Graded Meshes

(2020) Xiangcheng Zheng et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Optimal-order error estimates of finite element approximations to variable-order time-fractional diffusion equations without regularity assumptions of the true solutions

(2020) Xiangcheng Zheng et al.   IMA JOURNAL OF NUMERICAL ANALYSIS

Variable-order space-fractional diffusion equations and a variable-order modification of constant-order fractional problems

(2020) Xiangcheng Zheng et al.   APPLICABLE ANALYSIS

A fast solver for spectral elements applied to fractional differential equations using hierarchical matrix approximation

(2020) Xianjuan Li et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

A fast method for variable-order Caputo fractional derivative with applications to time-fractional diffusion equations

(2020) Zhi-Wei Fang et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications

(2019) HongGuang Sun et al.   Fractional Calculus and Applied Analysis

Wellposedness and regularity of the variable-order time-fractional diffusion equations

(2019) Hong Wang et al.   JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Block structured preconditioners in tensor form for the all–at–once solution of a finite volume fractional diffusion equation

(2019) D. Bertaccini et al.   APPLIED MATHEMATICS LETTERS

Analysis and numerical solution of a nonlinear variable-order fractional differential equation

(2019) Hong Wang et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

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

(2019) Jinhong Jia et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

On the fractional diffusion-advection-reaction equation in ℝ

(2019) Victor Ginting et al.   Fractional Calculus and Applied Analysis

Regularity of the solution to 1-D fractional order diffusion equations

(2018) V. J. Ervin et al.   MATHEMATICS OF COMPUTATION

On Time-Fractional Diffusion Equations with Space-Dependent Variable Order

(2018) Yavar Kian et al.   ANNALES HENRI POINCARE

Fast Iterative Method with a Second-Order Implicit Difference Scheme for Time-Space Fractional Convection–Diffusion Equation

(2017) Xian-Ming Gu et al.   JOURNAL OF SCIENTIFIC COMPUTING

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

(2017) Yongshan Li et al.   MATHEMATICAL METHODS IN THE APPLIED SCIENCES

A Splitting Preconditioner for Toeplitz-Like Linear Systems Arising from Fractional Diffusion Equations

(2017) Xue-lei Lin et al.   SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS

Fast preconditioned iterative methods for finite volume discretization of steady-state space-fractional diffusion equations

(2016) Jianyu Pan et al.   NUMERICAL ALGORITHMS

A preconditioned fast finite volume scheme for a fractional differential equation discretized on a locally refined composite mesh

(2015) Jinhong Jia et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Variational formulation of problems involving fractional order differential operators

(2015) Bangti Jin et al.   MATHEMATICS OF COMPUTATION

A Generalized Spectral Collocation Method with Tunable Accuracy for Variable-Order Fractional Differential Equations

(2015) Fanhai Zeng et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

A Fast Finite Element Method for Space-Fractional Dispersion Equations on Bounded Domains in $\mathbb{R}^2$

(2015) Ning Du et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Inhomogeneous Dirichlet Boundary-Value Problems of Space-Fractional Diffusion Equations and their Finite Element Approximations

(2014) Hong Wang et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

(2013) S. Chen et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Fast alternating-direction finite difference methods for three-dimensional space-fractional diffusion equations

(2013) Hong Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A superfast-preconditioned iterative method for steady-state space-fractional diffusion equations

(2012) Hong Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Fast Summation by Interval Clustering for an Evolution Equation with Memory

(2012) William McLean   SIAM JOURNAL ON SCIENTIFIC COMPUTING

A Fast Finite Difference Method for Two-Dimensional Space-Fractional Diffusion Equations

(2012) Hong Wang et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion

(2011) Changpin Li et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

A direct O(Nlog2N) finite difference method for fractional diffusion equations

(2010) Hong Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Variable-order fractional differential operators in anomalous diffusion modeling

(2009) HongGuang Sun et al.   PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS

Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term

(2009) P. Zhuang et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Finite Element Method for the Space and Time Fractional Fokker–Planck Equation

(2008) Weihua Deng   SIAM JOURNAL ON NUMERICAL ANALYSIS