Global Journal of Researches in Engineering, I: Numerical Methods, Volume 23 Issue 1

© 2023. Alexey S. Dorokhov, Solomashkin Alexey Alekseevich, Vyacheslav A. Denisov & Kataev Yuri Vladimirovich. This research/review article is distributed under the terms of the Attribution-NonCommercial-NoDerivatives 4.0 International (CC BYNCND 4.0). You must give appropriate credit to authors and reference this article if parts of the article are reproduced in any manner. Applicable licensing terms are at https://creativecommons.org/licenses/by-nc-nd/4.0/. Global Journal of Researches in Engineering: I Numerical Methods Volume 23 Issue 1 Version 1.0 Year 2023 Type: Double Blind Peer Reviewed International Research Journal Publisher: Global Journals Online ISSN: 2249-4596 & Print ISSN: 0975-5861 Application of Differentialintegral Functions By Alexey S. Dorokhov, Solomashkin Alexey Alekseevich, Vyacheslav A. Denisov & Kataev Yuri Vladimirovich Summary- The article is devoted to the development and implementation of new mathematical functions, differentialintegral functions that provide differentiation and integration operations not only according to existing algorithms described in textbooks on higher mathematics, but also by substituting a certain parameter k into formulas developed in advance, forming the necessary derivatives and integrals from these formulas. The Purpose of the Research: The expansion of the concept of number, in particular, in classical mechanics, physics, optics and other sciences, including biological and economic, which makes it possible to expand some understanding of the essence of space, time and their derivatives. Materials and Methods: The idea of fractional space, time and its application is given. The usual elementary functions and the Laplace transform were chosen as the object of research. New functions, differentialintegral functions, have been developed for them. A graphical representation of these functions is given, based on the example of the calculation of the sine wave. Examples of calculating these functions for elementary functions are given. Keywords: differentialintegral functions, derivative, fractional derivative, integral, fractional integral. ApplicationofDifferentialintegralFunctions Strictly as per the compliance and regulations of: GJRE-I Classification: ACM: (G.1), (G.2), (G.4), (F.1)