A time-fractional diffusion equation with space-time dependent hidden-memory variable order: analysis and approximation
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Publication:2665554
DOI10.1007/s10543-021-00861-4OpenAlexW3157686638MaRDI QIDQ2665554
Publication date: 19 November 2021
Published in: BIT (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10543-021-00861-4
regularityerror estimateswell-posednesstime-fractional diffusion equationL-1 discretizationspace-time dependent variable order
Initial-boundary value problems for second-order parabolic equations (35K20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Initial value problems for PDEs with pseudodifferential operators (35S10) Numerical analysis (65-XX)
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Cites Work
- Fractional integration and differentiation of variable order: an overview
- Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
- A generalized Gronwall inequality and its application to a fractional differential equation
- Convolution quadrature and discretized operational calculus. I
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- On time-fractional diffusion equations with space-dependent variable order
- On the time-fractional Schrödinger equation: theoretical analysis and numerical solution by matrix Mittag-Leffler functions
- On the maximum principle for a time-fractional diffusion equation
- A robust kernel-based solver for variable-order time fractional PDEs under 2D/3D irregular domains
- Variable order and distributed order fractional operators
- Existence, uniqueness and regularity of the solution of the time-fractional Fokker-Planck equation with general forcing
- Well-posedness of time-fractional advection-diffusion-reaction equations
- Temporal second order difference schemes for the multi-dimensional variable-order time fractional sub-diffusion equations
- Wellposedness and smoothing properties of history-state-based variable-order time-fractional diffusion equations
- A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications
- Time-stepping discontinuous Galerkin methods for fractional diffusion problems
- Finite difference/spectral approximations for the time-fractional diffusion equation
- A fully discrete difference scheme for a diffusion-wave system
- Wellposedness and regularity of the variable-order time-fractional diffusion equations
- Error Analysis of a High Order Method for Time-Fractional Diffusion Equations
- Wellposedness of Variable-Coefficient Conservative Fractional Elliptic Differential Equations
- Uniform convergence for a discontinuous Galerkin, time-stepping method applied to a fractional diffusion equation
- Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations
- A Generalized Spectral Collocation Method with Tunable Accuracy for Variable-Order Fractional Differential Equations
- Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
- A Space-Time Spectral Method for the Time Fractional Diffusion Equation
- Correction of High-Order BDF Convolution Quadrature for Fractional Evolution Equations
- Numerical Analysis of Nonlinear Subdiffusion Equations
- Sharp convergence rates of time discretization for stochastic time-fractional PDEs subject to additive space-time white noise
- Regularity of the solution to 1-D fractional order diffusion equations
- Gaussian Estimates and Holomorphy of Semigroups
- Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term
- Well-posedness and numerical approximation of a fractional diffusion equation with a nonlinear variable order
- Optimal-order error estimates of finite element approximations to variable-order time-fractional diffusion equations without regularity assumptions of the true solutions
- An Error Estimate of a Numerical Approximation to a Hidden-Memory Variable-Order Space-Time Fractional Diffusion Equation
- The Convergence of Collocation Solutions in Continuous Piecewise Polynomial Spaces for Weakly Singular Volterra Integral Equations
- Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
- Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions
- Subdiffusion with a time-dependent coefficient: Analysis and numerical solution
- Galerkin Finite Element Methods for Parabolic Problems
- Stochastic models for fractional calculus
- Analysis of fractional differential equations
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
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