A new generalized integral transform and applications

TL;DR

This paper introduces a new generalized integral transform that encompasses many known transforms, explores its properties, and demonstrates its application in solving boundary value problems, extending previous results.

Contribution

The work presents a novel integral transform with broad applicability, including properties, relationships with existing transforms, and practical problem-solving methods.

Findings

The new transform includes many known transforms as special cases.

Properties such as existence, scaling, and inversion are established.

Applied to solve initial boundary value problems with successful examples.

Abstract

In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence theorem, the scaling property, elimination property a Parseval-type identity, and inversion formula. The relationships of the new transform with well-known transforms are characterized by integral identities. The new transform is applied to solve certain initial boundary value problems. Some illustrative examples are given. The results established in this work extend and generalize recently published results.