Hyers-Ulam-Rassias Stability for a First Order Functional Differential Equation

Abstract

Abstract. In this paper, by using the fixed point method, we prove two new results on the Hyers-Ulam-Rassias and the Hyers-Ulam stability for the first order delay differential equation of the form ( ) ( , ( ), ( )). y t F t y t y t τ ′ = −Our results improve some related results in the literature.

Stability of delay differential equations in the sense of Ulam on unbounded intervals

“…by Tun and Bier [35]. They obtained the following significant result for delay differential equations.…”

“…In this paper, we will extend and improve these result by proving the stability results for delay differential equations for unbounded intervals. To achive stability results on unbounded intervals, we will use the inspiring techniques used in the above mentioned papers [7] and [35].…”

“…In 2015, by using the fixed point method, Tunç and Biçer [35] proved two new results on the Hyers-Ulam-Rassias and the Hyers-Ulam stability for the first-order delay differential equation…”

Hyers-Ulam-Rassias stability of non-linear delay differential equations

“…In recent years, Hyers-Ulam stability and Hyers-Ulam-Rassias stability of delay differential equations have attracted interest of researchers; see, for instance, [6,7,11,20,22]. One of the main reasons for this lies in the fact that, as pointed out by Kuang [13], delay differential equations arise in a number of applied problems in natural sciences and engineering.…”

“…For details on applications we recommend the monograph by Kuang [13]. Note that the results reported in [6,7,11,20,22] are concerned with stability of several classes of first-order non-linear and linear delay differential equations. Thereinto, Huang et al [7] recently proved the Hyers-Ulam stability for first non-linear delay differential equations on a compact interval.…”