In this article, we define the fractional Mellin transform by using Riemann-Liouville fractional integral operator and Caputo fractional derivative of order [Formula: see text] and study some of their properties. Further, some properties are extended to fractional way for Mellin transform.
Keywords: Caputo fractional derivative; Fractional calculus; Mellin transform; Riemann–Liouville fractional integral and derivative.