An optimization algorithm has been developed to study the effectiveness of substituting time tested ODEs with FDEs as applied to ship motions, specifically with an eye toward modeling different forms of roll damping. Relations between the order of differentiation a and damping coefficient b in the FDEs have been drawn for changing damping, added moment of inertia, and initial roll angle. A pitch model has also been studied and compared to the roll model. The error at each of these a and b pairs has also been calculated using an L2-norm. An initial effort was made to correlate the FDE coefficients to differing mechanisms of roll damping as characterized by Himeno.