A Hyers-Ulam Stability Analysis for Classes of Bessel Equations

Abstract

Mathematical modeling helps us to better understand different natural phenomena. Modeling is most of the times based on the consideration of appropriate equations (or systems of equations). Here, differential equations are well-known to be very useful instruments when building mathematical models -- specially because that the use of derivatives offers several interpretations associated with real life laws. Differential equations are classified based on several characteristics and, in this way, allow different possibilities of building models. In this paper we will be concentrated in analysing certain stability properties of classes of Bessel differential equations. In fact, the main aim of this work is to seek adequate conditions to derive different kinds of stabilities for the Bessel equation and for the modified Bessel equation by considering a perturbation of the trivial solution. In this way, sufficient conditions are obtained in order to guarantee Hyers-Ulam-Rassias, $\sigma$-semi-Hyers-Ulam and Hyers-Ulam stabilities for those equations.