scholarly journals Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3260
Author(s):  
Daniela Marian
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Delay Differential Equations ◽  
The Laplace Transform ◽  
Delay Differential ◽  
Rassias Stability

In this paper, we study semi-Hyers–Ulam–Rassias stability and generalized semi-Hyers–Ulam–Rassias stability of differential equations x′t+xt−1=ft and x″t+x′t−1=ft,xt=0ift≤0, using the Laplace transform. Our results complete those obtained by S. M. Jung and J. Brzdek for the equation x′t+xt−1=0.

scholarly journals On existence and stability results for nonlinear fractional delay differential equations

2018 ◽  
Vol 36 (4) ◽  
pp. 55-75 ◽  
Author(s):  
Kishor D. Kucche ◽  
Sagar T. Sutar
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Delay Differential Equations ◽  
Successive Approximation Method ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Existence And Stability ◽  
Fractional Delay ◽  
Delay Differential ◽  
Rassias Stability

We establish existence and uniqueness results for fractional order delay differential equations. It is proved that successive approximation method can also be successfully applied to study Ulam--Hyers stability, generalized Ulam--Hyers stability, Ulam--Hyers--Rassias stability, generalized Ulam--Hyers--Rassias stability, $ \mathbb{E}_{\alpha}$--Ulam--Hyers stability and generalized $ \mathbb{E}_{\alpha}$--Ulam--Hyers stability of fractional order delay differential equations.

A New Look at the Stability Analysis of Delay-Differential Equations

2005 ◽  
Author(s):  
Tama´s Kalma´r-Nagy
Keyword(s):  
Difference Equation ◽  
Differential Equations ◽  
Characteristic Equation ◽  
Delay Differential Equations ◽  
Linear Delay ◽  
The Laplace Transform ◽  
Method Of Steps ◽  
The Difference ◽  
The Stability ◽  
Delay Differential

It is shown that the method of steps for linear delay-differential equations combined with the Laplace-transform can be used to determine the stability of the equation. The result of the method is an infinite dimensional difference equation whose stability corresponds to that of the transcendental characteristic equation. Truncations of this difference equation are used to construct numerical stability charts. The method is demonstrated on a first and second order delay equation. Correspondence between the transcendental characteristic equation and the difference equation is proved for the first order case.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

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