Non-integer order of Bessel's equation

Question

I was introduced to Bessel's equation in class: $x^2 y'' + xy' + (x^2-p^2)y = 0$ where $p$ is a constant, not necessarily an integer. I want to ask what does $p$ in the Bessel function not being an integer, say complex number, possibly mean? It's hard to wrap my head around the idea that the order of Bessel Function can be a non-integer.