"Man Transform": A New Integral Transform with its applications to the Evaluation of Definite Integrals

Integral transforms, which convert initial value problems and some integral equations into algebraic equations that can be solved by applying the inverse transforms, are an important tool for solving these problems. Lately, a number of integral transformations have been Sumudu, Natural, Al-Tememe, Elzaki, Aboodh, T Kashuri and Fundo, Mahgoub, Kamal, Polynomial, Al-Zughair, Rangaig, Mohand, and Al-Zughair Transforms are among the initial value issues and certain integral equations that are demonstrated and used. The integral transform, which belongs to the Laplace integral transform class and is connected to the Jafari general integral transform, has been introduced and examined in this study. Additionally, various applications and theorems for resolving initial value issues have been supplied.