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Title: α-Mellin Transform and One of Its Applications
Authors: Nikolova, Yanka
Keywords: integral transforms method
Mellin transformation
Riemann-Liouville fractional derivative
fractional Bessel differential equation
Issue Date: 2012
Publisher: Bulgarian Academy of Sciences - National Committee for Mathematics
Citation: Mathematica Balkanica New Series, Vol. 26, Fasc 1-2 (2012), 185p-190p
Abstract: 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 [5], 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 [5]. Now we prove some further properties of this integral transform, useful for its application to solving some fractional order differential equations.
Description: MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45
ISSN: 0205-3217
Appears in Collections:Mathematica Balkanica New Series, Vol. 26, 2012, Fasc. 1-2

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