Mixed Fractional Heat Equation Driven by Fractional Brownian Sheet and Lévy Process

Abstract

We consider the stochastic heat equation of the form / = (Δ + Δ ) + ( / )( , , ) + ( , , )̇+̇, wherėis the fractional noise,̇is a (pure jump) Lévy space-time white noise, Δ is Laplacian, and Δ = −(−Δ) /2 is the fractional Laplacian generator on R, and , : [0, ] × R × R → R are measurable functions. We introduce the existence and uniqueness of the solution by the fixed point principle under some suitable assumptions.