{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:52:38Z","timestamp":1760230358799,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,21]],"date-time":"2022-07-21T00:00:00Z","timestamp":1658361600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Van Lang University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The paper\u2019s main purpose is to find the unknown source function for the conformable heat equation. In the case of (\u03a6,g)\u2208L2(0,T)\u00d7L2(\u03a9), we give a modified Fractional Landweber solution and explore the error between the approximate solution and the desired solution under a priori and a posteriori parameter choice rules. The error between the regularized and exact solution is then calculated in Lq(D), with q\u22602 under some reasonable Cauchy data assumptions.<\/jats:p>","DOI":"10.3390\/sym14071490","type":"journal-article","created":{"date-parts":[[2022,7,21]],"date-time":"2022-07-21T22:38:50Z","timestamp":1658443130000},"page":"1490","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Reconstructing the Unknown Source Function of a Fractional Parabolic Equation from the Final Data with the Conformable Derivative"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3041-8726","authenticated-orcid":false,"given":"Omid","family":"Nikan","sequence":"first","affiliation":[{"name":"School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1925-4601","authenticated-orcid":false,"given":"Ho Duy","family":"Binh","sequence":"additional","affiliation":[{"name":"Division of Applied Mathematics, Thu Dau Mot University, Thu Dau Mot City 75000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2257-1798","authenticated-orcid":false,"given":"Zakieh","family":"Avazzadeh","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Xi\u2019an Jiaotong-Liverpool University, Suzhou 215123, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8805-4588","authenticated-orcid":false,"given":"Le Dinh","family":"Long","sequence":"additional","affiliation":[{"name":"Division of Applied Mathematics, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City 700000, Vietnam"},{"name":"Faculty of Applied Technology, School of Engineering and Technology, Van Lang University, Ho Chi Minh City 700000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.cjph.2018.12.010","article-title":"Physical properties of the projectile motion using the conformable derivative","volume":"58","author":"Alharbia","year":"2019","journal-title":"Chin. 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