Abstract
This paper presents the exact solutions of the homogeneous and the non-homogeneous fractional delay oscillation equations with order α∈(1,2). For non-homogeneous fractional delay oscillation equation, the Laplace transform is taken up as solving method in that it efficiently avoids some restrictions to the non-homogeneous term. Thereafter, we investigate the Hyers–Ulam stability of the fractional delay oscillation equation.
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