Matlab fast fourier transform (FFT) function and time in hours frequency : hertz or millihertz?
That function is not periodic. Using the Fourier transform to analyze its behaviour is questionable, to say the least. Maybe you're confusing things with the Laplace transform, which is more useful when analyzing control systems?

Why should the axis in your plot have Hertz as unit?

The discrete Fourier transform¹ does a base transform from a vector in $C^N$ to a vector in $C^N$; its physical significance is that the result is that each bin represents another frequency between $0$ and the the Nyquist rate (which, in the complex sampling case is the sample rate, and in the real sampling case is half the sample rate).

Since you only have a real function, I'd argue frequencies are relative to $\frac{f_{sample}}2$.

$f_{sample}$ is $\frac{4}{\text{hour}}=\frac4{60\cdot60\,\text{s}}= \frac1{900}\,\text{Hz}$ in your case. So each bin represents a frequency $$f\in [-\frac{f_{sample}}2 ; \frac{f_{sample}}2[\,=\,[-\frac{1}{1800}\,\text{Hz}; \frac{1}{1800}\,\text{Hz}[$$.

Now, frequency base vectors are uniformly spread over the nyquist rate, so the $n^\text{th}$ bin represents frequency $\frac{\frac{1}{900}\,\text{Hz}}{n_\text{bins}}$. $n_\text{bins}$ is the number of bins, which is the same as the input vector size; which is $4\cdot24=96$. So each bin is $\frac1{96\cdot900}\,\text{Hz}= 11.5741\,\mu\text{Hz}$. Not very handy.

I think you're somewhat confused what an FFT is. I think a textbook on signal theory will do you very well!

¹ you're using fft, which is a fast implementation of the DFT; not the continuous Fourier transform. That's an important difference.