Hyers-Ulam Stability of First Order Nonhomogeneous Linear Dynamic Equations on Time Scales (Communications in Mathematical Research, 2019)
This paper deals with the Hyers-Ulam stability of the nonhomogeneous linear dynamic equation $x^{Δ}(t)-a x(t)=f(t)$, 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