A Class of Nonlinear Space–Time Fractional Kirchhoff‐Type Diffusion Equations With Delay

ABSTRACT In this paper, we study a class of nonlinear space–time fractional Kirchhoff‐type diffusion equations when the external force contains hereditary characteristics involving bounded and unbounded delays. Firstly, the well‐posedness of the problem is analyzed in phase space by using the Galerkin method and energy estimations. Furthermore, based on a corollary of the Brouwer fixed point theorem, the existence and uniqueness of the stationary solution of the problem are established. In addition, we also discuss the stability of the unique stationary solution.