The locus of the zeros of trigonometric functions under differintegration (Q2731626)

The zeros of the \(n\)-th derivative of the sine function are located equidistant on the real line. Replacing the derivative by a fractional derivative, the question is posed to locate the zeros of \(\sin^{(\nu)}(x)\) for noninteger \(\nu\), and of the other trigonometric functions. It turns out that the locus of the zeros form interesting patterns whose dynamics may prove to be worth in some modeling applications.