Hyers-Ulam-Rassias-Wright Stability for Fractional Oscillation Equation

Abstract

In this paper, we consider the nonhomogeneous fractional delay oscillation equation with order$\sigma$and introduce a class of control functions, i.e., Wright functions. Next, we apply the Cădariu-Radu method to prove the existence of a unique solution and Hyers-Ulam-Rassias-Wright stability of the fractional delay oscillation equation. At the end of the article, by an example, we show the application of the obtained results.