In this paper, we present an extended understanding of the term “applied mathematics,” a philosophy of mathematical modeling, the concept of a continuous mathematical model, three different approaches to constructing continuous mathematical models of real-world phenomena, and the concept of power laws and their use in modeling. The main message is that power laws are similar to constitutive laws and, when necessary, should be incorporated into an existing model describing real-world phenomena in a similar manner. Incorporating a power law into an existing model merely by replacing a temporal integer-order derivative with a temporal fractional-order derivative violates impulse conservation and affects the objectivity and consistency of the resulting model.