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Citation - WoS: 6
Citation - Scopus: 7
On Generalized Space of Quaternions and Its Application To a Class of Mellin Transforms
(int Scientific Research Publications, 2016) Baleanu, Dumitru; Al-Omari, Shrideh Khalaf Qasem
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.
Citation - WoS: 27
Extension of the Fractional Derivative Operator of the Riemann-Liouville
(int Scientific Research Publications, 2017) Agarwal, Praveen; Parmar, Rakesh K.; Alqurashi, Maysaa M.; Salahshour, Soheil; Baleanu, Dumitru
By using the generalized beta function, we extend the fractional derivative operator of the Riemann-Liouville and discusses its properties. Moreover, we establish some relations to extended special functions of two and three variables via generating functions. (C) 2017 All rights reserved.

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