Stochastic fractional partial differential equations driven by Poisson white noise (Q936465)

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.