Abstract
In this paper, we consider the stability problem of delay differential equations in the sense of Hyers-Ulam-Rassias. Recently this problem has been solved for bounded intervals, our result extends and improve the literature by obtaining stability in unbounded intervals. An illustrative example is also given to compare these results and visualize the improvement.
Highlights
Rassias [5] provided a remarkable generalization, which known as Hyers-Ulam-Rassias stability to
The first result on Hyers-Ulam stability of differential equations was given by Obloza [13, 14]
|y′(t) − F (t, y(t), y(t − τ ))| < φ(t), t ∈ [t0, T ], |y(t) − Ψ(t)| < φ(t), t ∈ [t0 − τ, t0], there exists a unique continuous function y0 : I0 → R satisfying Eq. As it is outlined in Introduction section, stability problem of differential equations in the sense of Hyers-Ulam was initiated by the papers of Obloza [13, 14]
Summary
Rassias [5] provided a remarkable generalization, which known as Hyers-Ulam-Rassias stability to-. The result of the Hyers-Ulam stability for first-order linear differential equations has been generalized by Miura et al [20], Takahasi et al [21] and Jung [22]. In 2015, by using the fixed point method, Tunc and Bicer [35] proved two new results on the Hyers-Ulam-Rassias and the Hyers-Ulam stability for the first-order delay differential equation y′(t) = F (t, y(t), y(t − τ )). Only in 2013, Andras and Meszaros [36] studied the Ulam-Hyers stability of some linear and nonlinear dynamic equations and integral equations on time scales They used both direct and operational methods. Jung [28] proved Hyers-Ulam stability as well as Hyers-Ulam-Rassias stability of the equation y′ = f (t, y) which extends the above mentioned results to nonlinear differential equations. |y′(t) − F (t, y(t), y(t − τ ))| < φ(t), t ∈ [t0, T ], |y(t) − Ψ(t)| < φ(t), t ∈ [t0 − τ, t0], there exists a unique continuous function y0 : I0 → R satisfying Eq
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