Analyses of solutions of Riemann-Liouville fractional oscillatory differential equations with pure delay

This paper first finishes off the exact solutions of Riemann-Liouville fractional differential time-delay oscillatory system of order rho is an element of(1,2)$$ \rho \in \left(1,2\right) $$ by using two newly defined delayed perturbations of Mittag-Leffler matrix functions and constant variation method. In the light of the exact solutions, we explore the finite time stability of the nonhomogeneous fractional oscillatory differential equations with pure delay. Ultimately, an example is cited to verify the rationality of the results. Through our method, the public problems left by Mahmudov in 2022 were partially solved.