{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T23:05:02Z","timestamp":1778627102954,"version":"3.51.4"},"reference-count":48,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T00:00:00Z","timestamp":1672790400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In applied sciences and engineering, partial differential equations (PDE) of integer and non-integer order play a crucial role. It can be challenging to determine these equations\u2019 exact solutions. As a result, developing numerical approaches to obtain precise numerical solutions to these kinds of differential equations takes time. The homotopy perturbation transform method (HPTM) and Yang transform decomposition method (YTDM) are the subjects of several recent findings that we describe. These techniques work well for fractional calculus applications. We also examine fractional differential equations\u2019 precise and approximative solutions. The Caputo derivative is employed because it enables the inclusion of traditional initial and boundary conditions in the formulation of the issue. This has major implications for complicated problems. The paper lists the important characteristics of the YTDM and HPTM. Our research has numerous applications in the disciplines of science and engineering and might be seen as a substitute for current methods.<\/jats:p>","DOI":"10.3390\/sym15010146","type":"journal-article","created":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T02:15:42Z","timestamp":1672798542000},"page":"146","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["A Comparative Study of Fractional Partial Differential Equations with the Help of Yang Transform"],"prefix":"10.3390","volume":"15","author":[{"given":"Muhammad","family":"Naeem","sequence":"first","affiliation":[{"name":"Department of Mathematics, Deanship of Applied Sciences, Umm Al-Qura University, Makkah 517, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0199-6850","authenticated-orcid":false,"given":"Humaira","family":"Yasmin","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, Preparatory Year Deanship, King Faisal University, Al-Ahsa 31982, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4306-8489","authenticated-orcid":false,"given":"Rasool","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nehad Ali","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0862-0648","authenticated-orcid":false,"given":"Jae Dong","family":"Chung","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,4]]},"reference":[{"key":"ref_1","unstructured":"Roberts, M. 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