On convolution for general novel fractional wavelet transform

TL;DR

This paper investigates the properties of the basic function related to the general novel fractional wavelet transform (GNFrWT), defining translation and convolution operations, and establishing existence theorems for these constructs.

Contribution

It introduces a new basic function for GNFrWT and develops the associated translation and convolution operations with proven existence theorems.

Findings

Defined the basic function $D^eta(u,v,w)$ for GNFrWT

Established properties and existence theorems for the basic function

Developed translation and convolution operations for GNFrWT

Abstract

Using Pathak and Pathak techniques, the basic function $D^\alpha(u,v,w)$ associated with general novel fractional wavelet transform (GNFrWT)is defined and its properties are investigated. By using basic function $D^\alpha(u,v,w)$ translation and convolution associated with GNFrWT are defined and certain existence theorems are proved for basic function and associated convolution.