Stochastic fractional partial differential equations driven by Poisson white noise
The aim of this paper is to study the existence, uniqueness and regularity of the solution of the following one-dimensional stochastic fractional partial differential equation given by \[ {\partial u\over\partial t} (t,x,w)= D^\alpha_\delta u(t,x,w)+ f(t,u(t,x))+ \int_U g(t,u(x), z)\widetilde N(dt,dx,dz), \] \[ u(0,x)= u_0(x) \] for \(t\in (0,+\infty)\), \(x\in\mathbb{R}\), where \((U,B(U),q)\) is a \(\sigma\) finite measure space, \(D^\alpha_\delta\) is the fractional differential operator with respect to special variable, \(f: (0,+\infty) \times \mathbb{R}\to\mathbb{R}\) and \(g: (0,+\infty)\times\mathbb{R}\times U\to\mathbb{R}\) are measurable.
stochastic partial differential equations
scientific article; zbMATH DE number 5312014