What allow matter wave propagation?

[TheCanadian]

If waves require a medium or some kind of force carrier to propagate, how exactly do matter waves propagate?

 

[Svein]

https://en.wikipedia.org/wiki/Wave_equation

 

[TheCanadian]

https://en.wikipedia.org/wiki/Wave_equation

Sorry. I'm just wondering what matter waves (e.g. $\lambda = \frac {h}{p}$) for an electron for example are classified as. How is an electron's wave inherently different than the wave represented by a photon or other elementary particle besides producing a different diffraction pattern? Do both waves propagate in any particular field (e.g. EM)? I guess I'm just trying to understand what it means for an electron to have a wave but I was under the assumption it also requires some kind of field, too.