The continuous fractional Bessel wavelet transform and its applications

Abstract

In this paper, the fractional Bessel wavelet transform is introduced by exploiting the theory of the fractional Hankel transform and the boundedness of the fractional Bessel wavelet transform obtained. Time invariant linear filter associated with the fractional Hankel transform is investigated and its various properties are obtained. In the present paper, authors also expressed time-invariant linear filters in the form of the fractional Bessel wavelet transform and applications of the aforesaid filters in the integral equation are given.

Keywords:

• Fractional Hankel transform
• continuous fractional Bessel wavelet transform
• Parseval formula
• fractional Hankel convolution
• Caldron reproducing formula
• time-invariant linear filters

2000 Mathematics Subject Classifications:

• 26A33
• 46F12
• 42C40
• 44A15
• 44A20

Acknowledgments

The authors are thankful to the referee for giving constructive criticism regarding the research work.

Disclosure statement

No potential conflict of interest is reported by the authors.

Additional information

Funding

This work is supported by SERB DST: MTR/2021/000266 and also financially supported by funding agency CSIR as a fellowship with CSIR-Ref No.: 09/1217(0043)/2018-EMR-I(CSIR-UGC NET-DEC. 2017).