We show how to solve a large class of Functional Differential Equations (FDEs) of the form

x'(t) = F(t,x(t),x(f(t)))

If the argument f(t) has certain properties then these equations are suitable for determining the initial conditions for problems from various fields such as control theory, traffic flow, spread of epidemics, and age-structured population growth. The required property on f is that it be idempotent, that is, f(f(t))=t. We extend the methods given here to apply to more general cases for f, solving equations that describe the behavior of a quantity whose reate of change depends upon several type of deviations of the time variable such as reverse time flows or periodic time flows, for example.

See Volume 6 Number 3  October 2003 issue of The Journal of Interdisciplinary Mathematics, pages 279-289

I will be happy to send interested parties a copy of a reprint of this article. E-mail me at clement.falbo@sonoma.edu.

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