Bulgarian Academy of Sciences - National Committee for Mathematics
Mathematica Balkanica New Series, Vol. 26, Fasc 1-2 (2012), 185p-190p
We consider a generalization of the classical Mellin transformation, called α-Mellin transformation, with an arbitrary (fractional) parameter α > 0. Here we continue the presentation from the paper , where we have introduced the definition of the α-Mellin transform and some of its basic properties. Some examples of special cases are provided. Its operational properties as Theorem 1, Theorem 2 (Convolution theorem) and Theorem 3 (α-Mellin transform of fractional R-L derivatives) are presented, and the proofs can be found in . Now we prove some further properties of this integral transform, useful for its application to solving some fractional order differential equations.