ANALYTICAL SOLUTION OF ABEL'S INTEGRAL EQUATION VIA NEW TRANSFORM SO-CALLED SADIK TRANSFORM WITH APPLICATIONS

Abstract

Abel's integral equation is an important type of integral equation that arises inmany areas of mathematics, physics, and engineering. For example, in tomography (specifically, in X-ray tomography or CT scans), the reconstruction of a function from its projectiondata can often be formulated as an Abel's integral equation. The equation helps reconstructthe radial density distribution of an object from its projections at various angles. So, theobjective of this study is to improve and develop the solve Abel's integral equation by usinga new transform so-called Sadik Transform. The main contributions include establishing and deriving sucient conditions to solve Abel's integral equation and generalized Abel's integral equation by recent Sadik Transform. In addition, some applications are made toexplain the solution procedure of Abel's integral equation by Sadik Transform.