Hyers-Ulam Stability of Bessel Equations

We analyse different kinds of stabilities for the Bessel equation and for the modified Bessel equation with initial conditions. Sufficient conditions are obtained in order to guarantee Hyers-Ulam-Rassias, $\sigma$-semi-Hyers-Ulam and Hyers-Ulam stabilities for those equations. Those sufficient conditions are obtained based on the use of integral techniques and majorations.