Abel dynamic equations of first and second kind

Abstract

AbstractThis paper gives the definition and analysis of Abel dynamic equations on a general time scale. As such, the results contain as special cases results for classical Abel differential equations and results for new Abel difference equations. By using appropriate transformations, expressions of Abel dynamic equations of second kind are derived on the general time scale. This also leads to a specific class of Abel dynamic equations of first kind. Finally, the canonical Abel dynamic equation is defined and examined.