{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T01:15:06Z","timestamp":1772327706838,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,16]],"date-time":"2025-04-16T00:00:00Z","timestamp":1744761600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union-Next Generation EU","award":["DUECOS BG-RRP-2.004-0001-C01"],"award-info":[{"award-number":["DUECOS BG-RRP-2.004-0001-C01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This article introduces a new fuzzy double integral transformation called fuzzy double Yang transformation. We review some of the main properties of the transformation and find the conditions for its existence. We prove the theorems for partial derivatives and fuzzy unitary convolution. All of the new results are applied to find an analytical solution to the fuzzy parabolic Volterra integro-differential equation (FPVIDE) with a suitably selected memory kernel. In addition, a numerical example is provided to illustrate how the proposed method might be helpful for solving FPVIDE utilizing symmetric triangular fuzzy numbers. Compared with other symmetric transforms, we conclude that our new approach is simpler and needs less calculations.<\/jats:p>","DOI":"10.3390\/sym17040606","type":"journal-article","created":{"date-parts":[[2025,4,16]],"date-time":"2025-04-16T10:04:56Z","timestamp":1744797896000},"page":"606","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Fuzzy Double Yang Transform and Its Application to Fuzzy Parabolic Volterra Integro-Differential Equation"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7377-9121","authenticated-orcid":false,"given":"Atanaska","family":"Georgieva","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6315-6238","authenticated-orcid":false,"given":"Slav I.","family":"Cholakov","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2194-6391","authenticated-orcid":false,"given":"Maria","family":"Vasileva","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-2535-4937","authenticated-orcid":false,"given":"Yordanka","family":"Gudalova","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1007\/BF02238819","article-title":"A finite difference method for analyzing the compression of poro-viscoelastic media","volume":"6","author":"Habetler","year":"1970","journal-title":"Computing"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1016\/0362-546X(88)90039-9","article-title":"Finite element methods for parabolic and hyperbolic partial integro-differential equations","volume":"12","author":"Yanik","year":"1988","journal-title":"Nonlinear Anal. 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