On generalized space of quaternions and its application to a class of Mellin transforms

Volume 9, Issue 6, pp 3898--3908 http://dx.doi.org/10.22436/jnsa.009.06.37

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Authors

Shrideh Khalaf Qasem Al-Omari - Department of Physics and Basic Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Amman 11134, Jordan. Dumitru Baleanu - Department of Mathematics, Cankaya University, Eskisehir Yolu 29.km, 06810 Ankara, Turkey. - cInstitute of Space Sciences, Magurele-Bucharest, Romania.

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.

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Keywords

• Mellin transform
• rotations
• quaternions
• Laplace transform
• Boehmians.

MSC

•  54C40
•  46F12

References

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