The Delayed Effect of Multiplicative Noise on the Blow-Up for a Class of Fractional Stochastic Differential Equations

Abstract

We investigated the blow-up of the weak solution to a class of fractional nonlinear stochastic differential equations driven by multiplicative noise in this paper. The a priori estimates and Galerkin method were applied to demonstrate the existence and uniqueness of the weak solution. Underlying the hypotheses of the nonlinear function and the initial data, for finite time, we prove that the solution does not blow up. Additionally, under further assumptions, we verified that the presence of multiplicative noise can delay the blow-up of the solution to infinity.

Keywords

• stochastic partial differential equation
• Caputo fractional derivative
• multiplicative noise
• blow-up