system
Given the following post, respond as if you're commenting on Reddit:
human
What are real-life applications to fractional and higher-order (specifically of degree 3+) derivatives?

I found this intriguing because the 4th, 5th, and 6th time-derivatives of displacement are snap, crackle, and pop, respectively--those names sound like they lack practical importance (apart from the cereal joke), at least to someone inexperienced like me.
gpt
They come up all the time in engineering or anything where you model a system with differential equations. 

In electrical circuits each reactive component in a circuit increases the degree of the differential equation that describes the transfer characteristics of the circuit. Quick example, an electric guitar's electronics can be modeled with a 3rd order differential equation, where the reactive components are the inductance of the pickup coil, the parasitic capacitance of the coil, and the tone cap. 

In control systems it's not uncommon to have higher order. In control systems you have some physical system called the plant, a feedback loop through a sensor, and a controller that takes the input of the feedback loop before feeding the system. The total closed loop system can be described by a differential equation, the order of which would be the sum of the orders of the controller, sensor transfer characteristics, and system. It can easily be 5-6th order even if you're approximating things. 

Another example, iirc the relationship of the roll control of an F16 with with the actual roll angle of the aircraft is 4th order. Someone may want to check me on that, it's often referenced when people bring up the fact that the aircraft is slightly unstable in order to turn faster. The controller is going to be at least 2nd order, so the total closed loop system is at least 6th order.