Fractional order integrators are like regular integrators, except they integrate things differently. A regular integrator (called an integer order integrator) adds together all the things you give it over time, making a total. A fractional order integrator runs the same process but adds smaller parts together, like fractions. It adds a series of fractions together instead of a single total. So instead of having a big number at the end, you get lots of little numbers that when added together make up the total.