Applying the natural transform iterative technique for fractional high-dimension equations of acoustic waves Laiq Zada 1 , Nasir Ali 1 , Rashid Nawaz 1 , Wasim Jamshed 2 *, Mohamed R. Eid 3,4 , El Sayed M. Tag El Din 5 , Hamiden Abd El- Wahed Khalifa 6,7 and Fayza Abdel Aziz ElSeabee 8,9 1 Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Pakistan, 2 Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad, Pakistan, 3 Department of Mathematics, Faculty of Science, New Valley University, Al-Kharga, Al-Wadi Al-Gadid, Egypt, 4 Department of Mathematics, Faculty of Science, Northern Border University, Arar, Saudi Arabia, 5 Electrical Engineering, Faculty of Engineering and Technology, Future University in Egypt, New Cairo, Egypt, 6 Department of Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt, 7 Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya, Saudi Arabia, 8 Mathematics Department, Faculty of Science, Helwan University, Cairo, Egypt, 9 Department of Mathematics, College of Science and Arts, Qassim University, Alasyah, Saudi Arabia In the present study, the natural transform iterative method (NTIM) has been implemented for the solution of a fractional Zakharavo–Kuznetsov (FZK) equation. NTIM is a relatively new technique for handling non-linear fractional differential equations. The method is tested upon the two non- linear FZK equalities. The solution of the proposed technique has been compared with the existing perturbation–iteration algorithm (PIA) method and residual power series method (RPSM). From the numerical results, it is clear that the method handles non-linear differential equations very suitably and provides the results in very closed accord with the accurate solution. As a result, the NTIM approach is regarded as one of the finest analytical techniques for solving fractional-order linear and non-linear problems. KEYWORDS natural transform method, fractional order differential equations (FDEs), approximate solution, acoustic waves, perturbation-iteration algorithm 1 Introduction Entropy and fractional calculus are appealing concepts that are increasingly being used to investigate the dynamics of complicated systems. Fractional calculus (FC) has been increasingly used in numerous sectors of research in recent years. Fractional differential equalities (FDEs) efficiently depict the natural evolution associated with viscoelasticity, models of porous electrodes, thermal stresses, electromagnetism, energy transmission in viscous dissipation systems, relaxing oscillations, and thermoelasticity. OPEN ACCESS EDITED BY Adnan, Mohi-ud-Din Islamic University, Pakistan REVIEWED BY Esra Karatas Akgül, Siirt University, Turkey Muhammad Farooq, University of Engineering and Technology, Pakistan *CORRESPONDENCE Wasim Jamshed, wasiktk@hotmail.com SPECIALTY SECTION This article was submitted to Process and Energy Systems Engineering, a section of the journal Frontiers in Energy Research RECEIVED 27 June 2022 ACCEPTED 09 August 2022 PUBLISHED 03 November 2022 CITATION Zada L, Ali N, Nawaz R, Jamshed W, Eid MR, Tag El Din ESM, Khalifa HAEW and ElSeabee FAA (2022), Applying the natural transform iterative technique for fractional high-dimension equations of acoustic waves. Front. Energy Res. 10:979773. doi: 10.3389/fenrg.2022.979773 COPYRIGHT © 2022 Zada, Ali, Nawaz, Jamshed, Eid, Tag El Din, Khalifa and ElSeabee. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. Frontiers in Energy Research frontiersin.org 01 TYPE Original Research PUBLISHED 03 November 2022 DOI 10.3389/fenrg.2022.979773