{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T12:41:46Z","timestamp":1771677706443,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T00:00:00Z","timestamp":1680220800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research (DSR), King Abdul Aziz University, Jeddah","award":["G-306-305-1442"],"award-info":[{"award-number":["G-306-305-1442"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this presented research, a hybrid technique is proposed for solving fourth-order (3+1)-D parabolic PDEs with time-fractional derivatives. For this purpose, we utilized the Elzaki integral transform with the coupling of the homotopy perturbation method (HPM). From performing various numerical experiments, we observed that the presented scheme is simple and accurate with very small computational errors.<\/jats:p>","DOI":"10.3390\/axioms12040347","type":"journal-article","created":{"date-parts":[[2023,4,3]],"date-time":"2023-04-03T02:10:13Z","timestamp":1680487813000},"page":"347","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Efficient Technique for Solving (3+1)-D Fourth-Order Parabolic PDEs with Time-Fractional Derivatives"],"prefix":"10.3390","volume":"12","author":[{"given":"Ramadan A.","family":"ZeinEldin","sequence":"first","affiliation":[{"name":"Deanship of Scientific Research, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}]},{"given":"Inderdeep","family":"Singh","sequence":"additional","affiliation":[{"name":"Department of Physical Sciences, Sant Baba Bhag Singh University (SBBSU), Jalandhar 144030, Punjab, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4278-2808","authenticated-orcid":false,"given":"Gurpreet","family":"Singh","sequence":"additional","affiliation":[{"name":"Department of Applied Sciences, Chitkara University Institute of Engineering and Technology, Rajpura 140401, Punjab, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1333-3862","authenticated-orcid":false,"given":"Mohammed","family":"Elgarhy","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Beni-Suef University, Beni-Suef 62521, Egypt"}]},{"given":"Hamiden Abd EI-Wahed","family":"Khalifa","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya 51951, Saudi Arabia"},{"name":"Department of Operations and Management Research, Cairo University, Giza 12613, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.chaos.2018.11.017","article-title":"Variational calculus involving nonlocal fractional derivative with Mittag\u2013Leffler kernel","volume":"118","author":"Chatibi","year":"2018","journal-title":"Chaos Solitons Fractals"},{"key":"ref_2","unstructured":"Podlubny, I. 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