aspg-21-2296-1791472224 20261008151024 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 23 1 Eman A. Mansour Departmnet of Electrical Technologies, Southern Technical University, Technical Institute Nasiriyah, Iraq Emad A. Kuffi Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, Iraq 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. 2024 323 334 2296 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.230127 https://www.americaspg.com/journal/21/article/2296 https://www.americaspg.com/storage/71702154419.pdf