数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (4): 1393-1410.

• 论文 • 上一篇    下一篇

ON THE FINITE MELLIN TRANSFORM IN QUANTUM CALCULUS AND APPLICATION

Bochra NEFZI, Kamel BRAHIM, Ahmed FITOUHI   

  1. Faculty of Sciences of Tunis, University of Tunis El Manar, Tunisia
  • 收稿日期:2016-02-01 修回日期:2017-10-25 出版日期:2018-08-25 发布日期:2018-08-25
  • 作者简介:Bochra NEFZI,E-mail:asimellinbochra@gmail.com;Kamel BRAHIM,E-mail:kamel.brahim@ipeit.rnu.tn;Ahmed FITOUHI,E-mail:ahmed.fitouhi@fst.rnu.tn

ON THE FINITE MELLIN TRANSFORM IN QUANTUM CALCULUS AND APPLICATION

Bochra NEFZI, Kamel BRAHIM, Ahmed FITOUHI   

  1. Faculty of Sciences of Tunis, University of Tunis El Manar, Tunisia
  • Received:2016-02-01 Revised:2017-10-25 Online:2018-08-25 Published:2018-08-25

摘要: The aim of the present paper is to introduce and study a new type of q-Mellin transform[11], that will be called q-finite Mellin transform. In particular, we prove for this new transform an inversion formula and q-convolution product. The application of this transform is also earlier proposed in solving procedure for a new equation with a new fractional differential operator of a variational type.

关键词: q-Mellin transform, finite Mellin transform, fractional q-integral, fractional q-differential equation

Abstract: The aim of the present paper is to introduce and study a new type of q-Mellin transform[11], that will be called q-finite Mellin transform. In particular, we prove for this new transform an inversion formula and q-convolution product. The application of this transform is also earlier proposed in solving procedure for a new equation with a new fractional differential operator of a variational type.

Key words: q-Mellin transform, finite Mellin transform, fractional q-integral, fractional q-differential equation