Mild solutions to time-fractional stochastic semi-linear wave equations
Author:
- 1 February 2025
- journal article
- Published by World Scientific Pub Co Pte Ltd in Stochastics and Dynamics
- Vol. 25 (01)
Abstract
Physical models that simulate viscoelastic phenomena with random effects often use stochastic wave equations, but to simulate viscoelastic phenomena depends on past random effects, stochastic wave equation with time-fractional derivative is the best choice. In this paper, we introduce a class of stochastic semi-linear wave equations with time-fractional derivatives, and study the existence, uniqueness, and the existence of continuous modification of mild solutions to this time-fractional stochastic semi-linear wave equation by establishing a prior estimation.Keywords
Funding Information
- National Science Foundation of China (12301606, 11501325, ZR2021QG036)
- Shandong Province Social Science Planning Research Project (24CJJJ18)
This publication has 29 references indexed in Scilit:
- On a terminal value problem for stochastic space‐time fractional wave equationsMathematical Methods in the Applied Sciences, 2022
- Mittag-Leffler Functions, Related Topics and Applications2020
- Error estimates of a semidiscrete finite element method for fractional stochastic diffusion‐wave equationsNumerical Methods for Partial Differential Equations, 2018
- Strong and Weak Approximation of Semilinear Stochastic Evolution Equations2014
- An L p -theory for stochastic integral equationsJournal of Evolution Equations, 2011
- Functional Fractional Calculus2011
- Vector-valued Laplace Transforms and Cauchy Problems2011
- Advances in Fractional Calculus2007
- Semigroups of operators, cosine operator functions, and linear differential equationsJournal of Mathematical Sciences, 1991
- Cosine families and abstract nonlinear second order differential equationsActa Mathematica Hungarica, 1978