Global Journal of Science Frontier Research, F: Mathematics and Decision Science, Volume 23 Issue 4

A New Integral Transform Called “Saxena & Gupta Transform” and Relation between New Transform and other Integral Transforms Hemlata Saxena α & Sakshi Gupta σ Author: Department of Mathematics, Career Point University, Kota(Rajasthan), India. e-mails: saxenadrhemlata@gmail.com, sakshigupta2397@gmail.com I. I ntroduction 1 Year 2023 9 Frontier Research Volume XXIII Issue ersion I V ( F ) Science © 2023 Global Journals Global Journal of Recently, Integral transformations have played an important role in many fields of science and engineering [1,10,14,15,], especially mathematical physics [5], engineering mathematics [16,19], Cryptography [11], image processing [18], mathematical electrodynamics [5] and, a few others, because they have been successfully used in solving many problems in those fields. Integral transforms are one of the most effective tools for solving problems in physics and engineering to obtain a solution for a given differential equation or integral equations by means of inverse transformation. The importance of an integral transforms is that they provide powerful operational methods for solving initial value problems and initial- boundary value problems for linear differential and integral equations. In view of many interesting properties which make visualization easier, we introduced a new integral transform, termed as "Saxena and Gupta" Transformation. Many of these transforms have been introduced which were extensively used and applied on theory and applications, such as Laplace [6,12,13,17], Fourier [15], Sumudu [4,12], Elzaki [3,8,9], Aboodh [2,19]. Among these, the most widely used is the Laplace transform. Here, a new integral transform is proposed to avoid the complexity of previous transforms. Abstract- We investigate a new integral transform called Saxena and Gupta transform, in this paper. Some important properties of this transform are also investigated. Also discussed relation between Saxena & Gupta transform and other integral transform like Laplace transform, Elzaki transform, Sumudu transform, Mahgoub transform. Integral transform of some elementary functions are given in table form in different section. R ef 11.Higgins, W. E. and D. C. Munson, (1988)."A Hankel transform approach to tomographic image reconstruction", IEEE Trans. Med. Imaging, vol. 7, pp 59-72. IV Keywords: New integral transform, Laplace transform, Elzaki transform, Sumudu transform, Mahgoub transform, Aboodh transform.