In this work, we introduce fractional Mellin transform of order $ \alpha, \ \ 0 \lt \alpha \leq1$ on a function which belongs to the Lizorkin space. Further, some properties and applications of fractional Mellin transform are given.
"On fractional order Mellin transform and some of its properties." Tbilisi Math. J. 10 (1) 315 - 324, Jan 2017. https://doi.org/10.1515/tmj-2017-0020