Open Access Research

The continuous fractional Bessel wavelet transformation

Akhilesh Prasad1, Ashutosh Mahato1, Vishal K Singh1 and Madan M Dixit2*

Author Affiliations

1 Department of Applied Mathematics, Indian School of Mines, Dhanbad, 826004, India

2 Department of Mathematics, NERIST, Nirjuli, India

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Boundary Value Problems 2013, 2013:40 doi:10.1186/1687-2770-2013-40

Published: 27 February 2013

Abstract

The main objective of this paper is to study the fractional Hankel transformation and the continuous fractional Bessel wavelet transformation and some of their basic properties. Applications of the fractional Hankel transformation (FrHT) in solving generalized nth order linear nonhomogeneous ordinary differential equations are given. The continuous fractional Bessel wavelet transformation, its inversion formula and Parseval’s relation for the continuous fractional Bessel wavelet transformation are also studied.

MSC: 46F12, 26A33.

Keywords:
Hankel transformation; fractional Hankel transformation; fractional Bessel wavelet transformation; Bessel function