ResearchArticle An Efficient Mathematical Approach for the Fraction Order Differentiation Based on Future Applications of Chaotic Parameter Ghulam Bary , 1 Waqar Ahmed , 2 Muhammad Sajid , 3 Riaz Ahmad , 1 Muhammad Farooq Saleem Khan, 4 Md Fayz-Al-Asad , 5 Nawaf N. Hamadneh , 6 and Ilyas Khan 7 1 Faculty of Science, Yibin University, Yibin 644000, Sichuan, China 2 Department of Bionanotechnology, Hanyang University, Ansan 155-88, Republic of Korea 3 Faculty of Materials and Chemical Engineering, Yibin University, Yibin 644000, Sichuan, China 4 Faculty of International Applied Technology, Yibin University, Yibin 64400, Sichuan, China 5 Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh 6 Department of Basic Sciences, College of Science and eoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia 7 Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al Majmaah 11952, Saudi Arabia Correspondence should be addressed to Ghulam Bary; ghulambary@gmail.com Received 17 August 2021; Accepted 22 September 2021; Published 16 October 2021 Academic Editor: Muhammad Shoaib Anwar Copyright © 2021 Ghulam Bary et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Normalized chaotic parameters examine the characterization of the particle production fluids produced at unusual energies and investigate a remarkable behavior in quantum measurement. e analogous characterization can be analyzed to probe the chaotic systems of boson particles creating sources of extraordinary energy. We observe that the bosons appear to be the appropriate aspirants of chaos fractions, and the normalized chaotic parameters evaluate the presence of such conglomerate phases sig- nificantly. e core point of this manuscript is that we calculate and examine the normalized chaotic parameters by differential equations to analyze the characteristics of the chaotic systems and their applications in thermal as well as in mechanical en- gineering. With such an efficient and distinctive approach, we perceive significant consequences for the correlator at higher temperature regimes. 1. Introduction e femtoscopy is extensively studied to investigate the characteristics of the chaotic and coherence systems created during the smashing of heavy nuclei at unprecedented energies [1–5]. e chaotic parameter is enormously used to extract the consequences of the hybrid systems under consideration that the boson particles are ejected usually from the partially chaotic sources to analyze the two particles interferometry. Such a unique chaotic parameter possesses the numerical values zero and one for the coherence and chaotic sources, respectively. On the other hand, it approaches unity for the chaotic emissions [1, 2, 6]. Moreover, various factors influence the lower order chaotic parameter like the misidentification of particles, laser emissions as well as the resonances of long-lived [1, 5, 7, 8]. Perpetually, two particles quantum interferences are de- termined experimentally to investigate the heat chaotic components and the coherence characterization. It is dis- tinguished; if the chaotic fraction is assessed more than fifty percent, then the two particles’ chaotic parameter suppresses roughly twenty-five percent ratio. is is the compelling cause to probe the chaotic and coherence properties asso- ciated with the produced systems using two particles Hindawi Mathematical Problems in Engineering Volume 2021, Article ID 7594496, 11 pages https://doi.org/10.1155/2021/7594496