{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,25]],"date-time":"2026-07-25T15:18:56Z","timestamp":1784992736279,"version":"3.55.0"},"reference-count":41,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,15]],"date-time":"2022-11-15T00:00:00Z","timestamp":1668470400000},"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>The main goal of this research is to present a new approach to double transforms called the double Laplace\u2013ARA transform (DL-ARAT). This new double transform is a novel combination of Laplace and ARA transforms. We present the basic properties of the new approach including existence, linearity and some results related to partial derivatives and the double convolution theorem. To obtain exact solutions, the new double transform is applied to several partial differential equations such as the Klein\u2013Gordon equation, heat equation, wave equation and telegraph equation; each of these equations has great utility in physical applications. In symmetry to other symmetric transforms, we conclude that our new approach is simpler and needs less calculations.<\/jats:p>","DOI":"10.3390\/sym14112418","type":"journal-article","created":{"date-parts":[[2022,11,16]],"date-time":"2022-11-16T02:31:27Z","timestamp":1668565887000},"page":"2418","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Using Double Integral Transform (Laplace-ARA Transform) in Solving Partial Differential Equations"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9905-5911","authenticated-orcid":false,"given":"Abdelilah Kamal","family":"Sedeeg","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Education, Holy Quran and Islamic Sciences University, Omdurman P.O. Box 14411, Sudan"},{"name":"Department of Mathematics, Faculty of Sciences and Arts-Almikwah, Albaha University, Al Bahah 65528, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zahra. I.","family":"Mahamoud","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences and Arts-Bukirayh, Alqassim University, Buraydah 52571, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Education, Omdurman Islamic University, Omdurman P.O. Box 382, Sudan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6394-1452","authenticated-orcid":false,"given":"Rania","family":"Saadeh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Zarqa University, Zarqa P.O. Box 2000, Jordan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"10197","DOI":"10.1016\/j.ijhydene.2019.02.162","article-title":"Importance of activation energy in development of chemical covalent bounding in flow of Sisko magneto-Nano fluids over porous moving curved surface","volume":"44","author":"Ahmad","year":"2019","journal-title":"Int. J. Hydrogen Energy."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2411","DOI":"10.1007\/s00542-018-4128-3","article-title":"Numerical simulation for MHD flow of Sisko nanofluid over a moving curved surface: A revised model","volume":"25","author":"Ahmad","year":"2019","journal-title":"Microsyst. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Constanda, C. (2002). 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