# α-Mellin Transform and One of Its Applications

Mathematica Balkanica New Series (2012)

- Volume: 26, Issue: 1-2, page 185-190
- ISSN: 0205-3217

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topNikolova, Yanka. "α-Mellin Transform and One of Its Applications." Mathematica Balkanica New Series 26.1-2 (2012): 185-190. <http://eudml.org/doc/281435>.

@article{Nikolova2012,

abstract = {MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45We 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.},

author = {Nikolova, Yanka},

journal = {Mathematica Balkanica New Series},

keywords = {integral transforms method; Mellin transformation; Riemann-Liouville fractional derivative; fractional Bessel differential equation},

language = {eng},

number = {1-2},

pages = {185-190},

publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},

title = {α-Mellin Transform and One of Its Applications},

url = {http://eudml.org/doc/281435},

volume = {26},

year = {2012},

}

TY - JOUR

AU - Nikolova, Yanka

TI - α-Mellin Transform and One of Its Applications

JO - Mathematica Balkanica New Series

PY - 2012

PB - Bulgarian Academy of Sciences - National Committee for Mathematics

VL - 26

IS - 1-2

SP - 185

EP - 190

AB - MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45We 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.

LA - eng

KW - integral transforms method; Mellin transformation; Riemann-Liouville fractional derivative; fractional Bessel differential equation

UR - http://eudml.org/doc/281435

ER -

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