  In this paper, we generalize the Riemann-Liouville differential and integral
operators on the space of Henstock-Kurzweil integrable distributions, $D_{HK}$.
We obtain new fundamental properties of the fractional derivative and integral,
a general version of the fundamental theorem of fractional calculus, semigroup
property for the Riemann-Liouville integral operators and relations between the
Riemann-Liouville integral and differential operators. Also, we achieve a
generalized characterization of the solution for the Abel integral equation.
Finally, we show relations for the Fourier transform of fractional derivative
and integral. These results are based on the properties of the distributional
Henstock-Kurzweil integral and convolution.
