{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T12:44:02Z","timestamp":1780058642792,"version":"3.54.0"},"reference-count":31,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,11,28]],"date-time":"2025-11-28T00:00:00Z","timestamp":1764288000000},"content-version":"vor","delay-in-days":331,"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 study investigates the existence, uniqueness, and stability of solutions to Riemann\u2013Liouville fractional differential equations with fractional variable\u2010order and antiperiodic boundary conditions. By employing the Banach fixed point theorem, we establish conditions for the uniqueness of solutions, while Schauder\u2019s fixed point theorem is used to prove their existence in a Banach space. We further demonstrate Ulam\u2013Hyers\u2013Rassias stability, ensuring solution robustness against perturbations. The variable\u2010order framework enables modeling of complex systems with evolving memory, offering advantages over constant\u2010order models in applications such as physics and epidemiology. A concrete example illustrates the practical applicability of our results. This work provides a rigorous theoretical foundation, bridging pure mathematics with potential applications in science and engineering, and sets the stage for future numerical and applied studies.<\/jats:p>","DOI":"10.1155\/jama\/8863599","type":"journal-article","created":{"date-parts":[[2025,11,28]],"date-time":"2025-11-28T15:20:28Z","timestamp":1764343228000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Analytical Study of Variable\u2010Order Fractional Differential Equations With Initial and Terminal Antiperiodic Boundary Conditions"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4342-5231","authenticated-orcid":false,"given":"Mohammed Said","family":"Souid","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2702-5112","authenticated-orcid":false,"given":"Zoubida","family":"Bouazza","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M\u2019hamed","family":"Bensaid","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9933-2624","authenticated-orcid":false,"given":"K. Sudar","family":"Mozhi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2504-5278","authenticated-orcid":false,"given":"Mokhtari","family":"Mokhtar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7066-246X","authenticated-orcid":false,"given":"Joshua Kiddy K.","family":"Asamoah","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2025,11,28]]},"reference":[{"key":"e_1_2_11_1_2","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/268347"},{"key":"e_1_2_11_2_2","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/691651"},{"key":"e_1_2_11_3_2","doi-asserted-by":"publisher","DOI":"10.1155\/2024\/5595720"},{"key":"e_1_2_11_4_2","doi-asserted-by":"publisher","DOI":"10.1142\/S1793524522501157"},{"key":"e_1_2_11_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2022.105189"},{"key":"e_1_2_11_6_2","doi-asserted-by":"publisher","DOI":"10.1155\/2024\/5168873"},{"key":"e_1_2_11_7_2","doi-asserted-by":"publisher","DOI":"10.3934\/math.2023038"},{"key":"e_1_2_11_8_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-021-03377-x"},{"key":"e_1_2_11_9_2","doi-asserted-by":"publisher","DOI":"10.3390\/axioms12010080"},{"key":"e_1_2_11_10_2","doi-asserted-by":"publisher","DOI":"10.3390\/axioms12040339"},{"key":"e_1_2_11_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.9748"},{"key":"e_1_2_11_12_2","doi-asserted-by":"publisher","DOI":"10.1063\/5.0206277"},{"key":"e_1_2_11_13_2","doi-asserted-by":"publisher","DOI":"10.3390\/fractalfract9020066"},{"key":"e_1_2_11_14_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13660-024-03249-4"},{"key":"e_1_2_11_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aej.2025.01.060"},{"key":"e_1_2_11_16_2","doi-asserted-by":"publisher","DOI":"10.22436\/jmcs.038.01.07"},{"key":"e_1_2_11_17_2","doi-asserted-by":"publisher","DOI":"10.1177\/01423312231164451"},{"key":"e_1_2_11_18_2","first-page":"482","article-title":"Solution of Fractional Differential Equations With Some Existence and Stability Results","volume":"12","author":"Ibrahim S.","year":"2023","journal-title":"Palestine Journal of Mathematics"},{"key":"e_1_2_11_19_2","volume-title":"Fractional Differential Equations","author":"Podlubny I.","year":"1999"},{"key":"e_1_2_11_20_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0300590"},{"key":"e_1_2_11_21_2","volume-title":"Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies","author":"Kilbas A. A.","year":"2006"},{"key":"e_1_2_11_22_2","doi-asserted-by":"publisher","DOI":"10.37256\/cm.5420245244"},{"key":"e_1_2_11_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01911126"},{"key":"e_1_2_11_24_2","first-page":"297","article-title":"Existence and Uniqueness Theorems for Nonlinear Coupled Boundary Value Problem of the A\n                  B\n                  C Fractional Differential Equation","volume":"37","author":"Janardhanan G.","year":"2025","journal-title":"Journal of Mathematics and Computer Science"},{"key":"e_1_2_11_25_2","doi-asserted-by":"publisher","DOI":"10.1080\/10652469308819027"},{"key":"e_1_2_11_26_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12190-025-02494-0"},{"key":"e_1_2_11_27_2","first-page":"93","article-title":"Approximate Solutions to Initial Value Problem for Differential Equation of Variable Order","volume":"9","author":"Zhang S.","year":"2018","journal-title":"Journal of Fractional Calculus and Applications"},{"key":"e_1_2_11_28_2","volume-title":"Fixed Point Theorems","author":"Smart D. R.","year":"1980"},{"key":"e_1_2_11_29_2","doi-asserted-by":"publisher","DOI":"10.1002\/asjc.3656"},{"key":"e_1_2_11_30_2","first-page":"103","article-title":"Ulam Stabilities of Ordinary Differential Equations in a Banach Space","volume":"26","author":"Rus I. A.","year":"2010","journal-title":"Carpathian Journal of Mathematics"},{"key":"e_1_2_11_31_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13661-025-01994-z"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/8863599","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/jama\/8863599","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/8863599","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T02:41:25Z","timestamp":1776393685000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/jama\/8863599"}},"subtitle":[],"editor":[{"given":"Mohammad Rezwan","family":"Habib","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10.1155\/jama\/8863599"],"URL":"https:\/\/doi.org\/10.1155\/jama\/8863599","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":"2025-05-14","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-10-17","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-11-28","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"8863599"}}