Abstract.

In this paper, we consider a nonlinear differential equation of second order including a variable deviating argument. In the noncanonical case, we investigate Hyers-Ulam stability of the considered differential equation on a finite interval. We prove three new theorems on the Ulam type stability. The proofs of the new outcomes of this paper are based on Banachs fixed point theorem. As the new contributions of the present paper, here, we improve and extend the outcomes that can be found in the earlier literature. The present paper also allows complementary outcomes for Hyers-Ulam stability of nonlinear differential equation of second order with and without deviating arguments. Finally, a concrete example with plots of the behaviours of solutions is given for illustrations.

Keywords:

deviating argument, generalization, Hyers-Ulam stability, second order, delay, linear differential equation