ON THE FINITE MELLIN TRANSFORM IN QUANTUM CALCULUS AND APPLICATION

Abstract

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

Bochra NEFZI, Kamel BRAHIM, Ahmed FITOUHI. ON THE FINITE MELLIN TRANSFORM IN QUANTUM CALCULUS AND APPLICATION[J].Acta mathematica scientia,Series B, 2018, 38(4): 1393-1410.

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