{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T19:56:53Z","timestamp":1775678213855,"version":"3.50.1"},"reference-count":34,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2022,10,15]],"date-time":"2022-10-15T00:00:00Z","timestamp":1665792000000},"content-version":"vor","delay-in-days":287,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"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":["Complexity"],"published-print":{"date-parts":[[2022,1]]},"abstract":"<jats:p>\n                    Excessive use of social media is a developing concern in the twenty\u2010first century. This issue needs to be addressed before it has any more significant consequences than what we are currently experiencing. As a preventive technique, advertisements and awareness\u2010raising campaigns about the detrimental impact of digital technologies are used. The application of novel mathematical techniques and terminologies in this field of study will have significant potential to enhance healthy living by preventing certain ailments. This is the most compelling justification for conducting a new study with the most up\u2010to\u2010date techniques at our disposal. This study investigates clear and concise transmission in order to generate a deterministic mathematical model of social media addiction  using the fractal\u2010fractional (FF) derivative operator. Also, the analysis of the  model in terms of the invariant domain, the existence of a positive invariant solution, and equilibria assumptions are stated in a detailed manner. Besides that, the basic reproduction number\n                    <jats:italic>\u211d<\/jats:italic>\n                    <jats:sub>0<\/jats:sub>\n                    &lt; 1 is computed, demonstrating that the proposed methodology is more efficacious. The Atangana\u2010Baleanu FF differential operators are recently defined in FF differential operators that are applied to characterize the  model\u2019s mathematical algorithm. We investigated the numerical behaviour of the  in three ways: (i) changing the fractional\u2010order (\n                    <jats:italic>\u03b1<\/jats:italic>\n                    ) as well as the fractal\u2010dimension (\n                    <jats:italic>\u2118<\/jats:italic>\n                    ); (ii) changing\n                    <jats:italic>\u03b1<\/jats:italic>\n                    while keeping\n                    <jats:italic>\u2118<\/jats:italic>\n                    constant; and (iii) changing\n                    <jats:italic>\u2118<\/jats:italic>\n                    while keeping\n                    <jats:italic>\u03b1<\/jats:italic>\n                    constant. Our examined visualizations and simulation studies using MATLAB for the numerical modelling of the aforementioned system showed that the novel developed Atangana\u2010Baleanu FF differential operators produce remarkable results when compared to the classical frame.\n                  <\/jats:p>","DOI":"10.1155\/2022\/2140649","type":"journal-article","created":{"date-parts":[[2022,10,15]],"date-time":"2022-10-15T10:05:06Z","timestamp":1665828306000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Nonlinear dynamics of the media addiction model using the fractal\u2010fractional derivative technique"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7137-1720","authenticated-orcid":false,"given":"Saima","family":"Rashid","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rehana","family":"Ashraf","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0808-4504","authenticated-orcid":false,"given":"Ebenezer","family":"Bonyah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2022,10,15]]},"reference":[{"key":"e_1_2_10_1_2","unstructured":"SmithA.andAndersonM. Social media Use 2018: Demographics and Statistics 2018 http:\/\/www.pewinternet.org\/2018\/03\/01\/social-media-use-in-2018."},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.2174\/13816128113199990617"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chb.2014.11.083"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chb.2015.09.007"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2021.110708"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2020.103560"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2020.105553"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.2174\/13816128113199990616"},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.1177\/1461444816671891"},{"key":"e_1_2_10_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.idm.2021.01.011"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1142\/3779"},{"key":"e_1_2_10_12_2","volume-title":"Theory and Application of Fractional Differential Equations","author":"Kilbas A.","year":"2006"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aej.2020.01.005"},{"key":"e_1_2_10_14_2","article-title":"A new definition of fractional derivative without singular kernel","volume":"73","author":"Caputo M.","year":"2015","journal-title":"Prog. Fract. Differ. Appl."},{"key":"e_1_2_10_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.03.054"},{"key":"e_1_2_10_16_2","volume-title":"Fractional Differential Equations","author":"Podlubny I.","year":"1999"},{"key":"e_1_2_10_17_2","doi-asserted-by":"publisher","DOI":"10.2298\/tsci160111018a"},{"key":"e_1_2_10_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2019.04.020"},{"key":"e_1_2_10_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2020.103771"},{"key":"e_1_2_10_20_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-020-02934-0"},{"key":"e_1_2_10_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2017.04.027"},{"key":"e_1_2_10_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.08.020"},{"key":"e_1_2_10_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijnonlinmec.2016.10.001"},{"key":"e_1_2_10_24_2","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/i2019-13003-7"},{"key":"e_1_2_10_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2022.105292"},{"key":"e_1_2_10_26_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-021-03515-5"},{"key":"e_1_2_10_27_2","doi-asserted-by":"publisher","DOI":"10.1023\/b:numa.0000027736.85078.be"},{"key":"e_1_2_10_28_2","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-021-03494-7"},{"key":"e_1_2_10_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0025-5564(02)00108-6"},{"key":"e_1_2_10_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2018.09.001"},{"key":"e_1_2_10_31_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.6200"},{"key":"e_1_2_10_32_2","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/938080"},{"key":"e_1_2_10_33_2","doi-asserted-by":"publisher","DOI":"10.2298\/fil1917691l"},{"key":"e_1_2_10_34_2","volume-title":"Fractional Stochastic Differential Equations","author":"Atangana A.","year":"2021"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2022\/2140649","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/2022\/2140649","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2022\/2140649","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T21:22:47Z","timestamp":1769116967000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2022\/2140649"}},"subtitle":[],"editor":[{"given":"Muhammad","family":"Ahmad","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2022,1]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["10.1155\/2022\/2140649"],"URL":"https:\/\/doi.org\/10.1155\/2022\/2140649","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1]]},"assertion":[{"value":"2022-06-09","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-07-21","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-10-15","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"2140649"}}