Mixed fractional heat equation driven by fractional Brownian sheet and Lévy process (Q1993166)

Summary: We consider the stochastic heat equation of the form \(\partial u / \partial t = (\Delta + \Delta_\alpha) u +(\partial f / \partial x)(t, x, u) + \sigma(t, x, u) \dot{L} + \dot{W}^H\), where \(\dot{W}^H\) is the fractional noise, \( \dot{L}\) is a (pure jump) Lévy space-time white noise, \( \Delta\) is Laplacian, and \(\Delta_\alpha = -(- \Delta)^{\alpha / 2}\) is the fractional Laplacian generator on \(\mathbb{R} \), and \(f, \sigma : [0, T] \times \mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R}\) are measurable functions. We introduce the existence and uniqueness of the solution by the fixed point principle under some suitable assumptions.