α-Mellin Transform and One of Its Applications

Nikolova, 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 -