After an introduction on the mathematical memory formalisms and on their use in many branches of science, we consider a model the evolutions of m > 2 economies yi(t), where we assume that their interaction is based on the differences of the values of their evolution status. Since the economies have bureaucratic structures that cause delays, we introduce in the equations a mathematical memory formalism represented by a derivative of fractional order, which leads to a system of integro-differential equations. The solution of the equations in the Laplace domain is presented as solution of a set of m linear equations in the Laplace Transform (LT) of the yi(t). It is found that the asymptotic values of the state of evolutions of the economies are equal. The case of a system of two economies with different memories is then considered obtaining their evolutions in the time domain expressed as simple monotonically decreasing closed form functions. The asymptotic values of their evolution are also found verifying that they are equal. Numerical and real examples are presented and discussed.
