Two-Dimensional Quaternionic Fractional Mellin Transform of a Particular Order

Abstract

Authorintroduces two-dimensionalquaternionic fractional Mellin transform defined for a particular order α,β of integrable functions on R2 and prove its inversion formula using the relation between fractional Fourier transform and fractional Mellin transform. Properties like linearity, Parseval’s formula and product theorem are obtained without any additional conditions. Applications of two dimensional quaternionic fractional Mellin transform are given to support the study.

Key words and phrases. Fractional calculus, Mellin transform, convolution, partial differential equation.

2010 Mathematics Subject Classification. 44A35, 44A05, 46S10