On generalized space of quaternions and its application to a class of Mellin transforms
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Date
2016
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Int Scientific Research Publications
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Abstract
The Mellin integral transform is an important tool in mathematics and is closely related to Fourier and bi-lateral Laplace transforms. In this article we aim to investigate the Mellin transform in a class of quaternions which are coordinates for rotations and orientations. We consider a set of quaternions as a set of generalized functions. Then we provide a new definition of the cited Mellin integral on the provided set of quaternions. The attributive Mellin integral is one-to-one, onto and continuous in the quaternion spaces. Further properties of the discussed integral are given on a quaternion context. (C) 2016 All rights reserved.
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Keywords
Mellin Transform, Rotations, Quaternions, Laplace Transform, Boehmians
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Citation
Al-Omari, Shrideh Khalaf Qasem; Baleanu, Dumitru, "On generalized space of quaternions and its application to a class of Mellin transforms", Journal of Nonlinear Sciences and Applications, Vol. 9, No. 6, pp. 3898-3908, (2016).
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Source
Journal of Nonlinear Sciences and Applications
Volume
9
Issue
6
Start Page
3898
End Page
3908