A numerical procedure for fractional-time-space differential equations with the spectral fractional Laplacian
DOI10.1007/978-981-19-7716-9_3MaRDI QIDQ6612885
Roberto Garrappa, Fabio V. Difonzo
Publication date: 1 October 2024
exponential time-differencing methodspectral fractional Laplacianeigendecompositionfractional-time-space differential equations
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Fractional derivatives and integrals (26A33) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) A priori estimates in context of PDEs (35B45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Fractional partial differential equations (35R11)
Cites Work
- Unnamed Item
- Fractional elliptic equations, Caccioppoli estimates and regularity
- A family of Adams exponential integrators for fractional linear systems
- The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
- Too much regularity may force too much uniqueness
- Ten equivalent definitions of the fractional Laplace operator
- On accurate product integration rules for linear fractional differential equations
- Generalized exponential time differencing methods for fractional order problems
- On the order of the error in discretization methods for weakly singular second kind Volterra integral equations with non-smooth solutions
- Inequalities in Fourier analysis
- Fractional operators with inhomogeneous boundary conditions: analysis, control, and discretization
- Detailed error analysis for a fractional Adams method
- Reformulation of elasticity theory for discontinuities and long-range forces
- Generalized exponential time differencing schemes for stiff fractional systems with nonsmooth source term
- Towards a unified theory of fractional and nonlocal vector calculus
- A data-driven peridynamic continuum model for upscaling molecular dynamics
- On the fractional Laplacian of variable order
- A space-time discretization of a nonlinear peridynamic model on a 2D lamina
- What is the fractional Laplacian? A comparative review with new results
- Three representations of the fractional \(p\)-Laplacian: semigroup, extension and Balakrishnan formulas
- Regularity of solutions to space-time fractional wave equations: A PDE approach
- Evaluation of generalized Mittag-Leffler functions on the real line
- A PDE Approach to Space-Time Fractional Parabolic Problems
- Regularity of spectral fractional Dirichlet and Neumann problems
- Finite element approximation of eigenvalue problems
- Exponential integrators
- Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions
- Runge-Kutta Theory for Volterra and Abel Integral Equations of the Second Kind
- The Fractional Laplacian
- Discretizations of the Spectral Fractional Laplacian on General Domains with Dirichlet, Neumann, and Robin Boundary Conditions
- Mittag-Leffler Functions, Related Topics and Applications
- The Fractional Laplacian
- Numerical Evaluation of Two and Three Parameter Mittag-Leffler Functions
- Computing Fractional Laplacians on Complex-Geometry Domains: Algorithms and Simulations
- Numerical methods for fractional diffusion
- An open-source parallel code for computing the spectral fractional Laplacian on 3D complex geometry domains
- A spectral method with volume penalization for a nonlinear peridynamic model
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