A New Integral Transform and Applications: HK-Transform.

In this paper, we propose a new integral transform called the HK Transform and employ it to analytically solve the Volterra integral equations (VIE.) of the first kind. To achieve this First we derive the HK transform of basic algebraic and transcendental mathematical functions. The fundamental characteristics of the HK transform, which can be used to solve a variety of functional equations, including, we then discuss the fundamental properties, such as ordinary differential equations and integral equations, then we discover the exact solution for general first class V.I.E. To illustrate the applicability of the HK transform, numerical problems are examined and handled carefully step-by-step. The results show that the proposed HK Transform new integral transform produces accurate solutions for first-kind VIE. without requiring time-consuming computations. [ABSTRACT FROM AUTHOR]