The Mayan Transform: A Novel Integral Transform of Complex Power Parameters and Applications to Neutrosophic Functions

Abstract

In this paper, a new type of integral transform with complex power parameters called the Mayan transform has been introduced. The definitions of the integral transform and its inverse are given in the classical case and the corresponding neutrosophic case. The classical analytical properties of the Mayan integral transforms are proven; the application of it to some essential functions and neutrosophic functions is introduced and proven. Also, its application to the neutrosophic derivatives (first, second, and third) then the generalization of the application on the Mayan integral transform on the neutrosophic derivatives are given. The worthiness of the introduced integral transform on the actual application is also proven by applying the integral transform in solving two problems: the response of an Undamped forced mechanical oscillator and the response of an undamped forced electrical oscillator.