On Another Type of Transform Called Rangaig Transform

Abstract

A new Integral Transform was introduced in this paper. Fundamental properties of this transform were derived and presented such as the convolution identity, and step Heaviside function. It is proven and tested to solve some basic linear-differential equations and had succesfully solved the Abel's Generalized equation and derived the Volterra Integral Equation of the second kind by means of Initial Value Problem. The Natural Logarithm (e.g logex=lnx) has been established and defined by means of modifying the Euler Definite Integral based on the Rangaig's fomulation. Hence, this transform may solve some different kind of integral and differential equations and it competes with other known transforms like Laplace, Sumudu and Elzaki Transform. Keywords: Rangaig Transform, Integral Transform, linear ordinary differential function, Integro-differential equation, Convolution Theorem.