Dynamics of fractional stochastic generalized Korteweg–de Vries–Burgers–Huxley equation with infinite memory

This paper is mainly concerned with a fractional stochastic generalized Korteweg–de Vries–Burgers–Huxley equation with infinite memory in a bounded domain. We first show the existence and uniqueness of solutions by contraction principle. Next, we investigate the stability properties to such kind of equation. Finally, we obtain the existence and uniqueness of weak D-pullback mean random attractors to fractional stochastic generalized Korteweg–de Vries–Burgers–Huxley equation with infinite memory. Interestingly, the fractional order Laplacian operator describes the non local dependency relationship of function values in integral form, and the decay rate of its kernel function is related to the order. The smaller the order, the stronger the non locality of the operator.