On the decomposition of solutions: from fractional diffusion to fractional Laplacian
From MaRDI portal
Publication:2059232
DOI10.1515/fca-2021-0066zbMath1498.35585OpenAlexW4206580277MaRDI QIDQ2059232
Publication date: 13 December 2021
Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/fca-2021-0066
regularityfractional Laplacianfractional diffusionRiemann-Liouville and Caputo derivativesdouble-sided
Fractional derivatives and integrals (26A33) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Fractional ordinary differential equations (34A08) Fractional partial differential equations (35R11)
Related Items (3)
Analysis of one-sided 1-D fractional diffusion operator ⋮ On the Dirichlet BVP of fractional diffusion advection reaction equation in bounded interval: structure of solution, integral equation and approximation ⋮ On the regularity and simplicity of a class of fractional elliptic operators
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Space-time fractional diffusion on bounded domains
- Hitchhiker's guide to the fractional Sobolev spaces
- Too much regularity may force too much uniqueness
- Accuracy of finite element methods for boundary-value problems of steady-state fractional diffusion equations
- Ten equivalent definitions of the fractional Laplace operator
- A high-accuracy preserving spectral Galerkin method for the Dirichlet boundary-value problem of variable-coefficient conservative fractional diffusion equations
- A simple finite element method for boundary value problems with a Riemann-Liouville derivative
- Eigenvalues of the fractional Laplace operator in the interval
- The asymptotic distribution of the eigenvalues for a class of Markov operators
- An introduction to Sobolev spaces and interpolation spaces
- Numerical simulation for conservative fractional diffusion equations by an expanded mixed formulation
- Fractals and fractional calculus in continuum mechanics
- Reanalysis of an open problem associated with the fractional Schrödinger equation
- Wellposedness of the two-sided variable coefficient Caputo flux fractional diffusion equation and error estimate of its spectral approximation
- Optimal Petrov-Galerkin spectral approximation method for the fractional diffusion, advection, reaction equation on a bounded interval
- Integral representation bound of the true solution to the BVP of double-sided fractional diffusion advection reaction equation
- A note on generalized Abel equations with constant coefficients
- Raising the regularity of generalized Abel equations in fractional Sobolev spaces with homogeneous boundary conditions
- On the fractional diffusion-advection-reaction equation in \(\mathbb{R}\)
- What is the fractional Laplacian? A comparative review with new results
- Regularity of the solution to fractional diffusion, advection, reaction equations in weighted Sobolev spaces
- Spectral approximation of a variable coefficient fractional diffusion equation in one space dimension
- Error estimates of a spectral Petrov-Galerkin method for two-sided fractional reaction-diffusion equations
- Error estimates of spectral Galerkin methods for a linear fractional reaction-diffusion equation
- The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
- Two-sided eigenvalue estimates for subordinate processes in domains
- Continuity of eigenvalues of subordinate processes in domains
- Wellposedness of Variable-Coefficient Conservative Fractional Elliptic Differential Equations
- On the consistency of the solutions of the space fractional Schrödinger equation
- Nonlocal Operators with Applications to Image Processing
- Variational solution of fractional advection dispersion equations on bounded domains in ℝd
- Distributions and Operators
- A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative
- A mixed‐type Galerkin variational formulation and fast algorithms for variable‐coefficient fractional diffusion equations
- Regularity of the solution to 1-D fractional order diffusion equations
- Image Denoising Methods. A New Nonlocal Principle
- Optimal Regularity and Error Estimates of a Spectral Galerkin Method for Fractional Advection-Diffusion-Reaction Equations
- On the nonlocality of the fractional Schrödinger equation
- Fractional Schrödinger equation for a particle moving in a potential well
- Comment on “On the consistency of the solutions of the space fractional Schrödinger equation” [J. Math. Phys. 53, 042105 (2012)]
- Variational formulation for the stationary fractional advection dispersion equation
- Variational formulation of problems involving fractional order differential operators
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
- Nonlocal equations in bounded domains: a survey
This page was built for publication: On the decomposition of solutions: from fractional diffusion to fractional Laplacian
