{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T03:42:11Z","timestamp":1776397331051,"version":"3.51.2"},"reference-count":34,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,9,7]],"date-time":"2025-09-07T00:00:00Z","timestamp":1757203200000},"content-version":"vor","delay-in-days":249,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>This article shows another display of the modified diffusion equation of fractional order involving Atangana\u2013Baleanu\u2013Caputo fractional derivative. The manuscript contains three major cases: the existence of a solution, uniqueness of the solution, and Hyers\u2013Ulam stability, which are discussed based on valid theorems in nonlinear analysis. Further, we present some examples to confirm our achievements.<\/jats:p>","DOI":"10.1155\/jama\/7940338","type":"journal-article","created":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T04:20:04Z","timestamp":1757305204000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Existence and Stability Results for a Modified Diffusion Equation Involving Atangana\u2013Baleanu\u2013Caputo Fractional Derivative"],"prefix":"10.1155","volume":"2025","author":[{"given":"Maral","family":"Sangi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5450-3127","authenticated-orcid":false,"given":"Mohammad Esmael","family":"Samei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,9,7]]},"reference":[{"key":"e_1_2_13_1_2","doi-asserted-by":"publisher","DOI":"10.3390\/fractalfract9080512"},{"key":"e_1_2_13_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2007.05.002"},{"key":"e_1_2_13_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2007.11.019"},{"key":"e_1_2_13_4_2","doi-asserted-by":"publisher","DOI":"10.1360\/012016-14"},{"key":"e_1_2_13_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2005.10.031"},{"key":"e_1_2_13_6_2","article-title":"Theory and Applications of Fractional Differential Equations","volume":"204","author":"Kilbas A. A.","year":"2006","journal-title":"North Holland Mathematics Studies"},{"key":"e_1_2_13_7_2","first-page":"101","article-title":"Essai sur L\u00e9tude des Fonctions Donn\u00e9es par Leur D\u00e9veloppement de Taylor","volume":"8","author":"Hadamard J.","year":"1892","journal-title":"Journal de Math\u00e9matiques Pures et Appliqu\u00e9es"},{"key":"e_1_2_13_8_2","first-page":"296","article-title":"Bemerkungen zum Begriff des Differentialquotienten Gebrochener Ordnung","volume":"62","author":"Weyl H.","year":"1917","journal-title":"Vierteljahrsschrift der Naturforschenden Gesellschaft in Z\u2136rich"},{"key":"e_1_2_13_9_2","doi-asserted-by":"publisher","DOI":"10.2298\/TSCI160111018A"},{"key":"e_1_2_13_10_2","doi-asserted-by":"publisher","DOI":"10.12785\/pfda\/010201"},{"key":"e_1_2_13_11_2","doi-asserted-by":"publisher","DOI":"10.3846\/mma.2025.22328"},{"key":"e_1_2_13_12_2","doi-asserted-by":"publisher","DOI":"10.3934\/math.2025294"},{"key":"e_1_2_13_13_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0311141"},{"key":"e_1_2_13_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12190-024-02122-3"},{"key":"e_1_2_13_15_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13661-024-01834-6"},{"key":"e_1_2_13_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2017.01.025"},{"key":"e_1_2_13_17_2","doi-asserted-by":"publisher","DOI":"10.1007\/s44198-022-00103-3"},{"key":"e_1_2_13_18_2","doi-asserted-by":"publisher","DOI":"10.22075\/ijnaa.2024.32641.4860"},{"key":"e_1_2_13_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(92)90074-W"},{"key":"e_1_2_13_20_2","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/24\/1\/015"},{"key":"e_1_2_13_21_2","doi-asserted-by":"publisher","DOI":"10.1186\/1029-242X-2011-81"},{"key":"e_1_2_13_22_2","doi-asserted-by":"publisher","DOI":"10.1186\/1687-1847-2012-36"},{"key":"e_1_2_13_23_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.7348"},{"key":"e_1_2_13_24_2","doi-asserted-by":"publisher","DOI":"10.1216\/jie.2024.36.317"},{"key":"e_1_2_13_25_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13661-022-01673-3"},{"key":"e_1_2_13_26_2","doi-asserted-by":"publisher","DOI":"10.3934\/math.20221071"},{"key":"e_1_2_13_27_2","doi-asserted-by":"publisher","DOI":"10.1155\/2022\/1812445"},{"key":"e_1_2_13_28_2","doi-asserted-by":"publisher","DOI":"10.3934\/math.2023610"},{"key":"e_1_2_13_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2018.10.006"},{"key":"e_1_2_13_30_2","doi-asserted-by":"publisher","DOI":"10.1080\/10652460310001600717"},{"key":"e_1_2_13_31_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-016-0949-5"},{"key":"e_1_2_13_32_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13660-017-1400-5"},{"key":"e_1_2_13_33_2","doi-asserted-by":"publisher","DOI":"10.2298\/FIL1717457A"},{"key":"e_1_2_13_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2006.05.061"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/7940338","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/jama\/7940338","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/7940338","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T02:44:51Z","timestamp":1776393891000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/jama\/7940338"}},"subtitle":[],"editor":[{"given":"Arpan","family":"Hazra","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10.1155\/jama\/7940338"],"URL":"https:\/\/doi.org\/10.1155\/jama\/7940338","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1]]},"assertion":[{"value":"2025-03-09","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-07-29","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-09-07","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"7940338"}}