{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:19:25Z","timestamp":1753881565012,"version":"3.41.2"},"reference-count":47,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,6,14]],"date-time":"2021-06-14T00:00:00Z","timestamp":1623628800000},"content-version":"vor","delay-in-days":164,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004054","name":"King Abdulaziz University","doi-asserted-by":"publisher","award":["D-146-130-1439"],"award-info":[{"award-number":["D-146-130-1439"]}],"id":[{"id":"10.13039\/501100004054","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>This article is dedicated to the existence results of solutions for boundary value problems of inclusion type. We suggest the infinite countable system to fractional differential inclusions written by . The mappings  are proposed to be Lipschitz multivalued mappings. The results are explored according to boundary condition <jats:italic>\u03c3<\/jats:italic><jats:italic>\u03bd<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>(0) = <jats:italic>\u03b3<\/jats:italic><jats:italic>\u03bd<\/jats:italic><jats:sub><jats:italic>i<\/jats:italic><\/jats:sub>(<jats:italic>\u03c1<\/jats:italic>), <jats:italic>\u2003<\/jats:italic>\u2009<jats:italic>\u03c3<\/jats:italic>, <jats:italic>\u03b3<\/jats:italic> \u2208 <jats:italic>\u211d<\/jats:italic>. This type of condition is the generalization of periodic, almost, and antiperiodic types.<\/jats:p>","DOI":"10.1155\/2021\/6653106","type":"journal-article","created":{"date-parts":[[2021,6,14]],"date-time":"2021-06-14T17:20:09Z","timestamp":1623691209000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Countable System of Fractional Inclusions with Periodic, Almost, and Antiperiodic Boundary Conditions"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8583-4228","authenticated-orcid":false,"given":"Ahmed","family":"Salem","sequence":"first","affiliation":[]},{"given":"Aeshah","family":"Al-Dosari","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,6,14]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00708-1"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2011.10.011"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.4153\/cmb-2011-170-7"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-016-1016-y"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.2298\/fil1711421m"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-019-2111-7"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.1215\/20088752-2018-0038"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2019.112355"},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.1239\/aap\/1059486824"},{"key":"e_1_2_10_10_2","doi-asserted-by":"publisher","DOI":"10.1214\/105051605000000070"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/bf01211070"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1017\/s0013091500020344"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jappmathmech.2013.12.002"},{"key":"e_1_2_10_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-00547-7"},{"key":"e_1_2_10_15_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-021-03302-2"},{"key":"e_1_2_10_16_2","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/8890575"},{"key":"e_1_2_10_17_2","doi-asserted-by":"publisher","DOI":"10.3390\/fractalfract4020018"},{"key":"e_1_2_10_18_2","doi-asserted-by":"publisher","DOI":"10.3390\/axioms9020059"},{"key":"e_1_2_10_19_2","doi-asserted-by":"publisher","DOI":"10.1080\/16583655.2020.1771834"},{"key":"e_1_2_10_20_2","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/9609108"},{"key":"e_1_2_10_21_2","doi-asserted-by":"publisher","DOI":"10.15388\/na.2019.6.3"},{"key":"e_1_2_10_22_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-018-1802-9"},{"key":"e_1_2_10_23_2","doi-asserted-by":"publisher","DOI":"10.11948\/20190419"},{"key":"e_1_2_10_24_2","doi-asserted-by":"publisher","DOI":"10.1155\/2020\/7345658"},{"key":"e_1_2_10_25_2","doi-asserted-by":"publisher","DOI":"10.57262\/die\/1584756017"},{"key":"e_1_2_10_26_2","doi-asserted-by":"publisher","DOI":"10.1080\/25742558.2020.1758361"},{"key":"e_1_2_10_27_2","doi-asserted-by":"publisher","DOI":"10.3390\/math7111030"},{"key":"e_1_2_10_28_2","doi-asserted-by":"publisher","DOI":"10.3390\/fractalfract3040051"},{"key":"e_1_2_10_29_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-93-86279-45-3"},{"key":"e_1_2_10_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247x(76)90248-1"},{"volume-title":"Geometric Properties of Banach Spaces and Nonlinear Lterations","year":"1965","author":"Chidume C.","key":"e_1_2_10_31_2"},{"volume-title":"Introduction To The Theory Of Differential Equations","year":"2002","author":"Georgi V.","key":"e_1_2_10_32_2"},{"key":"e_1_2_10_33_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-69512-4"},{"volume-title":"Set-Valued Analysis,","year":"1990","author":"Aubin J. P.","key":"e_1_2_10_34_2"},{"volume-title":"Multi-Valued Differential Equations","year":"2011","author":"Deimling K.","key":"e_1_2_10_35_2"},{"key":"e_1_2_10_36_2","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1975-124-2"},{"key":"e_1_2_10_37_2","doi-asserted-by":"publisher","DOI":"10.2307\/2274654"},{"key":"e_1_2_10_38_2","doi-asserted-by":"publisher","DOI":"10.2298\/tsci160111018a"},{"key":"e_1_2_10_39_2","unstructured":"Al-RefaiM. Fractional differential equations involving caputo fractional derivative with mittag-leffler non-singular kernel: comparison principles and applications Electronic Journal of Differential Equations 2017 2018 no. 36."},{"key":"e_1_2_10_40_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2017.12.003"},{"key":"e_1_2_10_41_2","doi-asserted-by":"publisher","DOI":"10.3389\/fphy.2019.00193"},{"key":"e_1_2_10_42_2","first-page":"175","volume-title":"On the Atangana-Baleanu Drivative and its Relation to Fading Memory Concept: The Diffusion Equation Formulation","author":"Hristov J.","year":"2019"},{"key":"e_1_2_10_43_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-019-2222-1"},{"key":"e_1_2_10_44_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1974-13640-2"},{"key":"e_1_2_10_45_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207160.2012.705280"},{"volume-title":"Convex Analysis and Measurable Multifunctions","year":"2006","author":"Castaing C.","key":"e_1_2_10_46_2"},{"key":"e_1_2_10_47_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-6359-4"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/6653106.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/6653106.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2021\/6653106","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T22:19:56Z","timestamp":1723241996000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2021\/6653106"}},"subtitle":[],"editor":[{"given":"Cristiana J.","family":"Silva","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":47,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1155\/2021\/6653106"],"URL":"https:\/\/doi.org\/10.1155\/2021\/6653106","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"2021-03-22","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-05-28","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-06-14","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"6653106"}}