{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T02:44:49Z","timestamp":1774579489719,"version":"3.50.1"},"reference-count":54,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T00:00:00Z","timestamp":1749081600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Deanship of Graduate Studies and Scientific Research at Qassim University for financial support","award":["QU-APC-2025"],"award-info":[{"award-number":["QU-APC-2025"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Fractional-order differential equations are prevalent in many scientific fields; hence, their study has seen a renaissance in recent years. The fascinating realm of fractional calculus is explored in this research study, with particular emphasis on the Harry Dym equation. To solve this problem, we use the Laplace Residual Power Series Method (LRPSM) and introduce the New Iterative Method (NIM). Both the mathematical complexity of the Harry Dym problem and the viability of the Caputo operator in this setting are investigated in our work. We go beyond the limitations of traditional mathematical methods to provide novel insights into the results of fractional-order differential equations via careful analysis and cutting-edge procedures. In this paper, we combine theory and practice to provide a novel perspective to the results of high-order fractional differential equations. Our efforts pay off by expanding our knowledge of mathematics and revealing the latent potential of the Harry Dym equation. This study expands researchers\u2019 and mathematicians\u2019 perspectives, bringing in a new and exciting period of progress in the field of fractional calculus.<\/jats:p>","DOI":"10.3390\/sym17060882","type":"journal-article","created":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T05:49:22Z","timestamp":1749102562000},"page":"882","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Analyzing the Harry Dym System Using the Laplace Residual Power Series Technique and New Iterative Technique with Caputo Derivative"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-3255-8630","authenticated-orcid":false,"given":"Muhammad","family":"Nasir","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Beihang University, Beijing 100191, China"}]},{"given":"Shuobing","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Beihang University, Beijing 100191, China"}]},{"given":"Hijaz","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, Republic of Korea"},{"name":"Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1466-8821","authenticated-orcid":false,"given":"Taha","family":"Radwan","sequence":"additional","affiliation":[{"name":"Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,5]]},"reference":[{"key":"ref_1","first-page":"91","article-title":"High order compact finite difference schemes for solving Bratu-type equations","volume":"5","author":"Gharechahi","year":"2019","journal-title":"J. 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