The discontinuous Galerkin finite element approximation of the multi-order fractional initial problems

DOI10.1016/j.amc.2018.11.057zbMath1428.82081OpenAlexW2904552076WikidataQ128705905 ScholiaQ128705905MaRDI QIDQ2008822

Zhengang Zhao, Yanfen Cui, Yunying Zheng

Publication date: 26 November 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2018.11.057

zbMATH Keywords

stabilityGalerkin finite element methodCaputo derivativediscontinuous Galerkin finite element methodmulti-order fractional differential equation

Mathematics Subject Classification ID

Transport processes in time-dependent statistical mechanics (82C70) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Finite element, Galerkin and related methods applied to problems in statistical mechanics (82M10)

Related Items (2)

Numerical approximation for fractional neutron transport equation ⋮ The time discontinuous space-time finite element method for fractional diffusion-wave equation

Cites Work

• Unnamed Item
• A study of nonlinear Langevin equation involving two fractional orders in different intervals
• The discontinuous Galerkin finite element method for fractional cable equation
• Langevin equation with two fractional orders
• High-order local discontinuous Galerkin method combined with WSGD-approximation for a fractional subdiffusion equation
• Numerical studies for a multi-order fractional differential equation
• Fractional high order methods for the nonlinear fractional ordinary differential equation
• V-Langevin equations, continuous time random walks and fractional diffusion
• Local discontinuous Galerkin method for a nonlinear time-fractional fourth-order partial differential equation
• Numerical methods for multi-term fractional (arbitrary) orders differential equations
• Detailed error analysis for a fractional Adams method
• An \(hp\) a priori error analysis of the DG time-stepping for initial value problems
• On the convergence of a new reliable algorithm for solving multi-order fractional differential equations
• A general finite element formulation for fractional variational problems
• On infinite order differential operators in fractional viscoelasticity
• Nonlinear fractional integro-differential Langevin equation involving two fractional orders with three-point multi-term fractional integral boundary conditions
• Adaptive discretization of fractional order viscoelasticity using sparse time history
• Applications of Fractional Calculus to the Theory of Viscoelasticity
• Stability of viscoelastic control systems
• Discontinuous Galerkin Methods for Ordinary Differential Equations
• Numerical solution of parabolic integro-differential equations by the discontinuous Galerkin method
• Fractional differentiation matrices with applications
• hp-Discontinuous Galerkin Time-Stepping for Volterra Integrodifferential Equations
• Variational formulation for the stationary fractional advection dispersion equation

This page was built for publication: The discontinuous Galerkin finite element approximation of the multi-order fractional initial problems