On the solutions of nonlinear stochastic fractional partial differential equations in one spatial dimension

Abstract

Existence, uniqueness and regularity of the trajectories of mild solutions of one-dimensional nonlinear stochastic fractional partial differential equations of order α > 1 containing derivatives of entire order and perturbed by space–time white noise are studied. The fractional derivative operator is defined by means of a generalized Riesz–Feller potential.