A new complex SEL integral transform and its applications on ordinary differential equations

Abstract

This paper introduces a new complex integral transformation obtained by inserting a complex parameter into the well-known Rangaig integral transform kernel function. The new integral transform is denoted by the acronym SEL and is called the Complex (Serifenur-Emad-Luay) integral transform. The proposed SEL integral transform features are explained and shown to correspond to some fundamental functions. The application of the SEL transform to finding the solution of some differential equations, including those arising in some real-world practical applications, is discussed as an illustration of the actual fields that could benefit from this novel transform.