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

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

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

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

A robust kernel-based solver for variable-order time fractional PDEs under 2D/3D irregular domains

(2019) Zhuo-Jia Fu et al.   APPLIED MATHEMATICS LETTERS

Finite element simulation and efficient algorithm for fractional Cahn–Hilliard equation

(2019) Feng Wang et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

A finite difference scheme on graded meshes for time-fractional nonlinear Korteweg-de Vries equation

(2019) Jinye Shen et al.   APPLIED MATHEMATICS AND COMPUTATION

A local radial basis function collocation method to solve the variable-order time fractional diffusion equation in a two-dimensional irregular domain

(2018) Song Wei et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Sharp Error Estimate of the Nonuniform L1 Formula for Linear Reaction-Subdiffusion Equations

(2018) Hong-lin Liao et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

On an accurate discretization of a variable-order fractional reaction-diffusion equation

(2018) Mojtaba Hajipour et al.   Communications in Nonlinear Science and Numerical Simulation

Non-Fickian diffusion of methanol in mesoporous media: Geometrical restrictions or adsorption-induced?

(2017) Alexey Zhokh et al.   JOURNAL OF CHEMICAL PHYSICS

Discrete maximal regularity of time-stepping schemes for fractional evolution equations

(2017) Bangti Jin et al.   NUMERISCHE MATHEMATIK

Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation

(2017) Martin Stynes et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Numerical simulation for conservative fractional diffusion equations by an expanded mixed formulation

(2016) Huanzhen Chen et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

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

(2016) Lueling Jia et al.   JOURNAL OF SCIENTIFIC COMPUTING

Numerical Solution of the Time-Fractional Fokker--Planck Equation with General Forcing

(2016) Kim Ngan Le et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

A PDE Approach to Space-Time Fractional Parabolic Problems

(2016) Ricardo H. Nochetto et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Activated desorption at heterogeneous interfaces and long-time kinetics of hydrocarbon recovery from nanoporous media

(2016) Thomas Lee et al.   Nature Communications

Second-order approximations for variable order fractional derivatives: Algorithms and applications

(2015) Xuan Zhao et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Solving the time-fractional Schrödinger equation by Krylov projection methods

(2015) Roberto Garrappa et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A new difference scheme for the time fractional diffusion equation

(2015) Anatoly A. Alikhanov   JOURNAL OF COMPUTATIONAL PHYSICS

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

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

Finite difference methods for the time fractional diffusion equation on non-uniform meshes

(2014) Ya-nan Zhang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Linking aquifer spatial properties and non-Fickian transport in mobile–immobile like alluvial settings

(2014) Yong Zhang et al.   JOURNAL OF HYDROLOGY

Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems

(2011) Kenichi Sakamoto et al.   JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation

(2011) Yuri Luchko   Fractional Calculus and Applied Analysis

An implicit finite-difference time-stepping method for a sub-diffusion equation, with spatial discretization by finite elements

(2010) K. Mustapha   IMA JOURNAL OF NUMERICAL ANALYSIS

Particle tracking for fractional diffusion with two time scales

(2009) Mark M. Meerschaert et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Discontinuous Galerkin method for an evolution equation with a memory term of positive type

(2009) Kassem Mustapha et al.   MATHEMATICS OF COMPUTATION

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

Time-fractional Diffusion of Distributed Order

(2008) Francesco Mainardi et al.   JOURNAL OF VIBRATION AND CONTROL