{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:29:50Z","timestamp":1760146190288,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,3]],"date-time":"2024-10-03T00:00:00Z","timestamp":1727913600000},"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 this article, the (p,q)-analogs of the \u03b1-th fractional Fourier transform are provided, along with a discussion of their characteristics in specific classes of (p,q)-generalized functions. Two spaces of infinitely (p,q)-differentiable functions are defined by introducing two (p,q)-differential symmetric operators. The (p,q)-analogs of the \u03b1-th fractional Fourier transform are demonstrated to be continuous and linear between the spaces under discussion. Next, theorems pertaining to specific convolutions are established. This leads to the establishment of multiple symmetric identities, which in turn requires the construction of (p,q)-generalized spaces known as (p,q)-Boehmians. Finally, in addition to deriving the inversion formulas, the generalized (p,q)- analogs of the \u03b1-th fractional Fourier transform are introduced, and their general properties are discussed.<\/jats:p>","DOI":"10.3390\/sym16101307","type":"journal-article","created":{"date-parts":[[2024,10,3]],"date-time":"2024-10-03T07:59:59Z","timestamp":1727942399000},"page":"1307","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On (p,q)-Analogs of the \u03b1-th Fractional Fourier Transform and Some (p,q)-Generalized Spaces"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8955-5552","authenticated-orcid":false,"given":"Shrideh","family":"Al-Omari","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 11134, Jordan"},{"name":"Jadara University Research Center, Jadara University, Irbid 21110, Jordan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-3742-6178","authenticated-orcid":false,"given":"Wael","family":"Salameh","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology, Abu Dhabi University, Abu Dhabi 59911, United Arab Emirates"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"305","DOI":"10.2307\/2370183","article-title":"q-difference equations","volume":"32","author":"Jackson","year":"1910","journal-title":"Amer. 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