A Petrov-Galerkin finite element method using polyfractonomials to solve stochastic fractional differential equations
DOI10.1016/j.apnum.2021.05.031zbMath1480.65245OpenAlexW3173403097WikidataQ115360308 ScholiaQ115360308MaRDI QIDQ2048420
Ali Foroush Bastani, Nazanin Abedini, Bijan Zohouri Zangeneh
Publication date: 5 August 2021
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.apnum.2021.05.031
Petrov-Galerkin methodstochastic fractional differential equationpolyfractonomialRiemann-Liouville fractional Brownian motion
Gaussian processes (60G15) Fractional processes, including fractional Brownian motion (60G22) Fractional derivatives and integrals (26A33) Inverse problems for PDEs (35R30) Applications of stochastic analysis (to PDEs, etc.) (60H30) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) PDEs with randomness, stochastic partial differential equations (35R60) Fractional partial differential equations (35R11) Regularization by noise (60H50)
Uses Software
Cites Work
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- Fractional Sturm-Liouville eigen-problems: theory and numerical approximation
- Exponentially accurate spectral and spectral element methods for fractional ODEs
- On a Burgers type nonlinear equation perturbed by a pure jump Lévy noise in \(\mathbb R^d\)
- Stochastic response of a class of self-excited systems with Caputo-type fractional derivative driven by Gaussian white noise
- A high-order discontinuous Galerkin method for Itô stochastic ordinary differential equations
- A general framework for simulation of fractional fields
- The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
- Intermittence and nonlinear parabolic stochastic partial differential equations
- Polynomial interpolation results in Sobolev spaces
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- Existence and uniqueness of solutions for stochastic differential equations of fractional-order \(q > 1\) with finite delays
- Error estimates of finite element methods for nonlinear fractional stochastic differential equations
- Random integral equations with applications to life sciences and engineering
- Stochastic Volterra equations with singular kernels
- New methods for simulation of fractional Brownian motion
- Existence of solutions for nonlinear fractional stochastic differential equations
- Asymptotic properties of the fractional Brownian motion of Riemann-Liouville type
- Lévy-driven stochastic Volterra integral equations with doubly singular kernels: existence, uniqueness, and a fast EM method
- A Galerkin finite element method for time-fractional stochastic heat equation
- A review of definitions of fractional derivatives and other operators
- Noise regularization and computations for the 1-dimensional stochastic Allen-Cahn problem
- Finite difference/spectral approximations for the time-fractional diffusion equation
- Stochastic fractional differential equations: modeling, method and analysis
- Well-posedness and EM approximations for non-Lipschitz stochastic fractional integro-differential equations
- Stochastic calculus for fractional Brownian motion and related processes.
- Numerical solution of stochastic fractional differential equations
- On the solutions of nonlinear stochastic fractional partial differential equations in one spatial dimension
- A spectral method for stochastic fractional differential equations
- Tempered fractional Brownian motion: wavelet estimation, modeling and testing
- An Introduction to Computational Stochastic PDEs
- Introduction to Uncertainty Quantification
- Existence result for fractional neutral stochastic integro-differential equations with infinite delay
- Simulating Sample Paths of Linear Fractional Stable Motion
- A Space-Time Spectral Method for the Time Fractional Diffusion Equation
- Finite element and difference approximation of some linear stochastic partial differential equations
- Fractional Diffusion Equations and Anomalous Diffusion
- Error estimates of a semidiscrete finite element method for fractional stochastic diffusion‐wave equations
- Solving Parametric Fractional Differential Equations Arising from the Rough Heston Model Using Quasi-Linearization and Spectral Collocation
- Numerical Solutions of Nonautonomous Stochastic Delay Differential Equations by Discontinuous Galerkin Methods
- The Mathematical Theory of Finite Element Methods
- Stochastic Calculus for Fractional Brownian Motion and Applications
- Variational formulation for the stationary fractional advection dispersion equation
- On the Convergence of Ordinary Integrals to Stochastic Integrals
- Fractional Brownian Motions, Fractional Noises and Applications
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
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