Al-Omari, Shrideh Khalaf QasemBaleanu, DumitruBaleanu, Dumitru2020-04-062020-04-062016Al-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).2008-18982008-1901https://doi.org/10.22436/jnsa.009.06.37Al-Omari, Shrideh/0000-0001-8955-5552The 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.eninfo:eu-repo/semantics/openAccessMellin TransformRotationsQuaternionsLaplace TransformBoehmiansArticle963898390810.22436/jnsa.009.06.372-s2.0-84990036874WOS:000386871300037N/AN/A