Fractional Derivative and Laplace Transform

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I've learned a lot with this lecture: https://www.youtube.com/watch?v=2FZlz4-pf-M.

I have a doubt at 14:17. Why did the professor putted the minus sign?

I also would like to know if the derivative that uses the Laplace transform is the Riemann-Liouville derivative. I think no, because if yes we could take a closed form to derivative...

So, if no in fact, has this kind of derivative some name?

Thank you so much if you could answer. Best regards.