On a class of nonlinear time‐fractional pseudo‐parabolic equations with bounded delay

Abstract

In the present paper, we study a class of nonlinear time‐fractional pseudo‐parabolic equations with bounded time‐delay. Firstly, we analyze the well‐posedness of the problem by the well‐known Galerkin's method and some compactness criteria. Next, the existence of the stationary solutions is established by utilizing a lemma of ours, which is a corollary of the Brouwer fixed point theorem. Finally, with regard to the stability analysis of the stationary solutions, we prove the local stability via the direct method of energy estimations and show the asymptotic stability by the construction of appropriate Lyapunov functionals.