Hyers–Ulam Stability of Order k for Euler Equation and Euler–Poisson Equation in the Calculus of Variations

In this paper, we define and study Hyers–Ulam stability of order 1 for Euler’s equation m−1 the Euler–Poisson in calculus variations two special cases, when these equations have form y″(x)=f(x) y(m)(x)=f(x), respectively. We prove some estimations Jyx−Jy0x, where y is an approximate solution y0 exact corresponding Euler Euler-Poisson equations, also give examples.