One-dimensional dynamical systems type delta over Integral Domains

In this paper, autonomous differential equations type delta of order one on integral domains are defined. For this we will use the autonomous ring defined on the Hurwitz expansion ring of exponential generating functions with coefficients in an integral domain. We will also use delta operators, which behave like derivatives when acting on polynomials, along with Umbral calculus. As a particular example of a delta operator we have the forward difference operator that defines the difference equations. Then the delta-type equations generalize to the ordinary equations and to the difference equations.