{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T17:19:29Z","timestamp":1773335969142,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,7,4]],"date-time":"2019-07-04T00:00:00Z","timestamp":1562198400000},"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>Two-dimensional advection\u2013diffusion processes with memory and a source concentrated in the symmetry center of the domain have been investigated. The differential equation of the studied model is a fractional differential equation with short-tail memory (a differential equation with Caputo\u2013Fabrizio time-fractional derivatives). An analytical solution of the initial-boundary value problem has been determined by employing the Laplace transform and double sine-Fourier transforms. A numerical solution of the studied problem has been determined using finite difference approximations. Numerical simulations for both solutions have been carried out using the software Mathcad.<\/jats:p>","DOI":"10.3390\/sym11070879","type":"journal-article","created":{"date-parts":[[2019,7,4]],"date-time":"2019-07-04T11:13:18Z","timestamp":1562238798000},"page":"879","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Two-Dimensional Advection\u2013Diffusion Process with Memory and Concentrated Source"],"prefix":"10.3390","volume":"11","author":[{"given":"Najma","family":"Ahmed","sequence":"first","affiliation":[{"name":"Abdus Salam School of Mathematical Sciences, Government College University, 5400 Lahore, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1949-5643","authenticated-orcid":false,"given":"Nehad Ali","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Lahore Leads University, 5400 Lahore, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9989-8452","authenticated-orcid":false,"given":"Dumitru","family":"Vieru","sequence":"additional","affiliation":[{"name":"Department of Theoretical Mechanics, Technical University \u201cGheorghe Asachi\u201d of Iasi, 6600 Iasi, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Mainardi, F. 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