Article ID: MTJPAM-D-24-00011

Title: A new modified integral transform and its applications

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-24-00011; Volume 6 / Issue 1 / Year 2024, Pages 85-101

Document Type: Research Paper

Author(s): Koray Biçer ^a , Ayşe Neşe Dernek ^b , Durmuş Albayrak ^c , Fatih Aylıkcı ^d

^aDepartment of Mathematics, Marmara University, Goztepe, Istanbul, Turkey

^bDepartment of Mathematics, Marmara University, Goztepe, Istanbul, Turkey

^cDepartment of Mathematics, Marmara University, Goztepe, Istanbul, Turkey

^dDepartment of Mathematical Engineering, Yıldız Technical University, Esenler, Istanbul, Turkey

Received: 20 January 2024, Accepted: 5 May 2024, Published: 27 May 2024

Corresponding Author: Ayşe Neşe Dernek (Email address: ndernek@marmara.edu.tr)

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Abstract

In this paper, the authors introduce a new integral transform ℳ_ν, n, 2 (Re(ν)>0, n∈ℤ⁺), which yields some useful new or known integral transforms as its special cases. Several theorems that are dealing with general properties of the ℳ_ν, n, 2-integral transform are proven. The existence theorem, convolution theorem and inversion theorem for ℳ_ν, n, 2-integral transform are given. Generalized Natural transform 𝒩₂⁺, which is a special form of ℳ_ν, n, 2-integral transform, is used to find solutions of some certain differential and integral equations. Also some illustrative examples like Bessel equation, Hermite equation are given to demonstrate the applicability of the results.

Keywords: Laplace transform, Natural transform, Borel-Dzrbashjan transform, Bessel differential equation, Hermite differential equation

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