Study of the results of Hilbert transformation for some fractional derivatives

Caputo Fractional Derivative is a base for the Riemann-Liouville Derivative, Katugampola fractional derivative, and other fractional derivatives. In this paper, we have illustrated several critical features of the Caputo Derivative via Hilbert Transformation that have not yet been discussed. We have also investigated the behavior of the Riemann-Liouville integral and studied the results of the <i>k</i>-Riemann-Liouville fractional integral with the applications of Hilbert transformation.