Variational stability results of dynamic equations on time-scales using generalized ordinary differential equations

Abstract

Generalized ordinary differential equations can be used to tackle the setback of the everywhere requirement of the existence of the integral of some functions of the dynamic equations on a time-scale. In this study, we investigated the variational stability and variational asymptotic stability of the zero solution of the dynamic equation on time-scale using the established results of the variational stability and variational asymptotic stability of the zero solution of the generalized ordinary differential equations as presented in this work. The regulated and rd-continuous assumptions on the integral function of the ∆ -integral of the dynamic equation on the time-scale equation enhanced the compatibility of the results. An example is used to illustrate the suitability of the results.