Anyone know how to do this, specifically for the following integral:
[$] \int_0^\infty \left( \frac{d^p}{dx^p} f(x) \right) \delta(x-k) dx [$]
where [$] 0< p < 1 [$].
I'm not sure how (fractional) integration by parts works and what the fractional derivative of the dirac delta function would be. Any thoughts and/or pointers to introductory papers on this appreciated. Thanks.