In formula 16 of the paper called "Fractional-order gradient descent learning of BP neural networks with Caputo derivative". (I attached the paper below) The single variable chain rule for the Caputo derivative is listed as:

\begin{equation}

D^{\alpha} f(s) = \frac{d}{ds} h(s) * D^{\alpha} s(t)

\end{equation}

where $f(s) = h(s(t))$

That is, when taking fractional order $\alpha$ derivative, we can take an integer order of the outside function, then pass the fractional order derivative operation to the inner function. However, when I try to do it for some explicitly function, it's off by some constant factor...

for example, you can try h(t) = t^2 and s(t) =t, and do the 1/2 order derivative.

I feel like the formula is correct but missing some constant factor, is that right? I am new in the area so any comments, advice would be greatly helpful.

Furthermore, if anyone can tell me where to find a good book on multivariable fractional calculus, that would be very helpful as well.

Thank you!