A New Integral Transform “Dukani Transform” with Applications

This paper describes a novel integral transform called the "Dukani Transform," which we can employ to precisely (analytically) solve the Volterra integral equations (VIE) of the first sort. To do this, first the Dukani transform of transcendental and elementary algebraic mathematical functions is derived by the authors. Next, the basic properties of the Dukani transform were discussed. Then, using a range of differential equations, including integral equations (IEs), ordinary differential equations (ODEs), and integro differential equations (IDEs), the exact (analytic) solution for first-class generic VIE was found by the authors. Numerical problems have been thoroughly examined and solved, in a step wise manner, demonstrating the applicability of the Dukani transform. The findings demonstrate that, without need for time-consuming calculations, the suggested "Dukani Transform" new integral transform produces accurate (VIEs.) of first-kind and second kind.