{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T11:47:38Z","timestamp":1762084058608,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T00:00:00Z","timestamp":1672272000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The main purpose of this study is to investigate solutions of some integral equations of different classes using a new scheme. This research introduces and implements the new double ARA transform to solve integral and partial integro-differential equations. We introduce basic theorems and properties of the double ARA transform in two dimensions, and some results related to the double convolution theorem and partial derivatives are presented. In addition, to show the validity of the proposed technique, we introduce and solve some examples using the new approach.<\/jats:p>","DOI":"10.3390\/computation11010004","type":"journal-article","created":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T03:19:46Z","timestamp":1672370386000},"page":"4","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Application of the ARA Method in Solving Integro-Differential Equations in Two Dimensions"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6394-1452","authenticated-orcid":false,"given":"Rania","family":"Saadeh","sequence":"first","affiliation":[{"name":"Department of Mathematics, Zarqa University, Zarqa 13110, Jordan"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,29]]},"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. 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