Analysis of time fractional and space nonlocal stochastic nonlinear Schrödinger equation driven by multiplicative white noise

DOI10.1016/j.jmaa.2018.06.066zbMath1392.60059OpenAlexW2838489883MaRDI QIDQ724718

Jiarui Liang, Tianlong Shen, Songhe Song, Xu Qian

Publication date: 26 July 2018

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2018.06.066

zbMATH Keywords

mild solutionnumerical schemeoptimal error estimatefractional Laplacian operatorCaputo-type time fractional derivative

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Fractional partial differential equations (35R11)

Related Items (6)

On inverse initial value problems for the stochastic strongly damped wave equation ⋮ Effective approximation for a nonlocal stochastic Schrödinger equation with oscillating potential ⋮ Fractional white noise functional soliton solutions of a Wick-type stochastic fractional NLSE ⋮ The stochastic nonlinear Schrödinger equation in unbounded domains and non-compact manifolds ⋮ A fast mass-conserving explicit splitting method for the stochastic space-fractional nonlinear Schrödinger equation with multiplicative noise ⋮ On initial value and terminal value problems for subdiffusive stochastic Rayleigh-Stokes equation

Cites Work

• A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications
• The time fractional Schrödinger equation on Hilbert space
• On the \(L_\infty \) convergence of a difference scheme for coupled nonlinear Schrödinger equations
• Fractional-time Schrödinger equation: fractional dynamics on a comb
• Stochastic nonlinear Schrödinger equations with linear multiplicative noise: rescaling approach
• Concentrating standing waves for the fractional Schrödinger equation with critical nonlinearities
• Space-time fractional Schrödinger equation with time-independent potentials
• Fractional quantum mechanics and Lévy path integrals
• Existence of invariant measures for the stochastic damped Schrödinger equation
• Approximate solution to the time-space fractional cubic nonlinear Schrödinger equation
• Mathematical theory and numerical methods for Bose-Einstein condensation
• Time fractional Schrödinger equation revisited
• Concentrating solutions of nonlinear fractional Schrödinger equation with potentials
• Existence of the global smooth solution to the period boundary value problem of fractional nonlinear Schrödinger equation
• Analysis of the damped nonlinear space-fractional Schrödinger equation
• The use of a meshless technique based on collocation and radial basis functions for solving the time fractional nonlinear Schrödinger equation arising in quantum mechanics
• Convergence of a \(\theta \)-scheme to solve the stochastic nonlinear Schrödinger equation with Stratonovich noise
• Neumann problem for nonlinear Schrödinger equation with the Riesz fractional derivative operator
• A mass-preserving splitting scheme for the stochastic Schrodinger equation with multiplicative noise
• Some physical applications of fractional Schrödinger equation
• Generalized fractional Schrödinger equation with space-time fractional derivatives
• Commutator estimates and the euler and navier-stokes equations
• Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation
• The Stochastic Nonlinear Schrödinger Equation inH¹
• Time fractional Schrödinger equation
• Time fractional Schrödinger equation: Fox's H-functions and the effective potential

This page was built for publication: Analysis of time fractional and space nonlocal stochastic nonlinear Schrödinger equation driven by multiplicative white noise