In this paper, the stabilities in the sense of Hyers–Ulam, Hyers–
Ulam–Rassias,Mittag–Leffler–Hyers–Ulam and Mittag–Leffler–Hyers–Ulam–
Rassias of n-th order linear differential equations are investigated. The
main results are proved by applying generalized replacement lemma and
generalized Gronwall’s inequality. The obtained results include many previous
results and give improvements. In particular, the results have improved
in two ways: no initial conditions for differential equations and
no conditions for a coefficient. Most of the results are limited to the case
where the interval is bounded, but a result for the unbounded case is
obtained.
