Abstract
Abstract This paper focuses on a novel method for the stability of fractional partial differential equations with a power fractional derivative. By some estimates of convex functions, we extend the Lyapunov functionals for ODE systems to their fractional-order counterparts with and without the Laplacian operator term. Accordingly, it is shown that the stability conditions in these systems can be derived from their integer-order equivalents. The efficiency of the proposed method is demonstrated through some applications.