Stability analysis of higher order nonlinear differential equations in <i>β</i>–normed spaces

Abstract

In this paper, we interrogate different Ulam type stabilities, ie, β –Ulam–Hyers stability, generalized β –Ulam–Hyers stability, β –Ulam–Hyers–Rassias stability, and generalized β –Ulam–Hyers–Rassias stability, for n th order nonlinear differential equations with integrable impulses of fractional type. The existence and uniqueness of solutions are investigated by using the Banach contraction principle. In the end, we give an example to support our main result.