The Fourier transform approach to Hyers-Ulam stability of differential equation of second order

Abstract

The use of Fourier transform has increased in the light of recent events in different application. Fourier transform is also seen as the easiest and an effective way among the other transformation. In line with this, the research deals with the Hyers-Ulam stability of second order differential equation using Fourier transform. The study aims at deriving a generalized Hyers-Ulam results for second order differential equations with constant co-efficient $\mathcal{H}″(v)+a\mathcal{H}\prime (v)+b\mathcal{H}(v)=r(t)$ with the help of Fourier Transform.