On the Convergence Result of the Fractional Pseudoparabolic Equation

Abstract

In this paper, we consider the nonlinear fractional Laplacian pseudoparabolic equation (NFLPPE). We mainly focus on the convergence of mild solutions with respect to the order of fractional Laplacian. By using many techniques, we obtain the result that the mild solution will converge when the fractional order of the Laplacian tends to $1^{-}$ . The proof of convergent result relies on sharp techniques of evaluating the exponential terms, the Sobolev embeddings, and weakly singular Gronwall inequalities.