Volume 35, Issue 2
Hyers-Ulam Stability of First Order Nonhomogeneous Linear Dynamic Equations on Time Scales

Commun. Math. Res., 35 (2019), pp. 139-148.

Published online: 2019-12

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• Abstract

This paper deals with the Hyers-Ulam stability of the nonhomogeneous linear dynamic equation $x^{\Delta}(t)-a x(t)=f(t)$, where $a\in\mathcal{R}^{+}$. The main results can be regarded as a supplement of the stability results of the corresponding homogeneous linear dynamic equation obtained by Anderson and Onitsuka (Anderson D R, Onitsuka M. Hyers-Ulam stability of first-order homogeneous linear dynamic equations on time scales. $Demonstratio$ $Math$., 2018, 51: 198–210).

• Keywords

Hyers-Ulam stability, ∆-derivative, time scale, linear dynamic equation

34D20, 34N05, 39A30

shenyonghong2008@hotmail.com (Yonghong Shen)

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@Article{CMR-35-139, author = {Shen , Yonghong and Li , Yongjin}, title = {Hyers-Ulam Stability of First Order Nonhomogeneous Linear Dynamic Equations on Time Scales}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {35}, number = {2}, pages = {139--148}, abstract = {

This paper deals with the Hyers-Ulam stability of the nonhomogeneous linear dynamic equation $x^{\Delta}(t)-a x(t)=f(t)$, where $a\in\mathcal{R}^{+}$. The main results can be regarded as a supplement of the stability results of the corresponding homogeneous linear dynamic equation obtained by Anderson and Onitsuka (Anderson D R, Onitsuka M. Hyers-Ulam stability of first-order homogeneous linear dynamic equations on time scales. $Demonstratio$ $Math$., 2018, 51: 198–210).

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2019.02.05}, url = {http://global-sci.org/intro/article_detail/cmr/13484.html} }
TY - JOUR T1 - Hyers-Ulam Stability of First Order Nonhomogeneous Linear Dynamic Equations on Time Scales AU - Shen , Yonghong AU - Li , Yongjin JO - Communications in Mathematical Research VL - 2 SP - 139 EP - 148 PY - 2019 DA - 2019/12 SN - 35 DO - http://doi.org/10.13447/j.1674-5647.2019.02.05 UR - https://global-sci.org/intro/article_detail/cmr/13484.html KW - Hyers-Ulam stability, ∆-derivative, time scale, linear dynamic equation AB -

This paper deals with the Hyers-Ulam stability of the nonhomogeneous linear dynamic equation $x^{\Delta}(t)-a x(t)=f(t)$, where $a\in\mathcal{R}^{+}$. The main results can be regarded as a supplement of the stability results of the corresponding homogeneous linear dynamic equation obtained by Anderson and Onitsuka (Anderson D R, Onitsuka M. Hyers-Ulam stability of first-order homogeneous linear dynamic equations on time scales. $Demonstratio$ $Math$., 2018, 51: 198–210).

Yong-hong Shen & Yong-jin Li. (2019). Hyers-Ulam Stability of First Order Nonhomogeneous Linear Dynamic Equations on Time Scales. Communications in Mathematical Research . 35 (2). 139-148. doi:10.13447/j.1674-5647.2019.02.05
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