I'm a little confused about what you're doing but I understand your arguments about sexp as a continuum product.

We have A beautiful result I would like to show:

We start with the two identities that are already proven by others working on fractional calculus.

And even more generally:

whree the convolution is done over s, and the values at t are the same for both f and g.

Therefore: if and

That means even more remarkably

That means

This has so much value for continuum sums. This is remarkable!

I have to properly justify this using the continuity of these operators over some hilbert space. That's the only way I can think of.

I would also like to standardize a notation that is very intuitive. If we take the continuum sum over the interval [a,b] we say:

This has all the linearity rules of the integral, and some own unique rules of its own.

We have A beautiful result I would like to show:

We start with the two identities that are already proven by others working on fractional calculus.

And even more generally:

whree the convolution is done over s, and the values at t are the same for both f and g.

Therefore: if and

That means even more remarkably

That means

This has so much value for continuum sums. This is remarkable!

I have to properly justify this using the continuity of these operators over some hilbert space. That's the only way I can think of.

I would also like to standardize a notation that is very intuitive. If we take the continuum sum over the interval [a,b] we say:

This has all the linearity rules of the integral, and some own unique rules of its own.