This document discusses optimizing the quality factor (Q-factor) of fractional order band-pass and band-stop filters. It presents expressions for the magnitude response of fractional order band-pass and band-stop filters with order less than two. A genetic algorithm is used to optimize the Q-factor by varying filter parameters like pole and zero locations. The algorithm finds optimal parameters to achieve a high Q-factor while maintaining symmetry of the magnitude response. The optimization approach is also applied to fractional second order filters, but these tend to reduce to first order filters when optimizing for high Q-factor. References are provided for further reading on fractional order filters and circuit implementations.