{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T07:26:13Z","timestamp":1770276373452,"version":"3.49.0"},"reference-count":23,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2023,8,9]],"date-time":"2023-08-09T00:00:00Z","timestamp":1691539200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Appl. Math. Stat."],"abstract":"<jats:p>Social media addiction (SMA) is the excessive use of social media platforms, resulting in negative consequences for individuals. It is characterized by an uncontrollable urge to use social media, leading to negative effects in human's life. This study aims to construct a mathematical model to conceptualize the transmission dynamics of SMA and explore the underlying mechanisms of this harmful addiction in the framework of fractional derivative. The fundamentals of fractional calculus are listed for examining the model. Equilibrium points are identified, and the reproduction parameter R<jats:sub>0<\/jats:sub> is computed to understand the dynamics of SMA spread. Stability analysis of the equilibria is performed, and the impact of various input parameters is numerically investigated. The existence and uniqueness of the proposed SMA model are demonstrated through simulations, which also study the intricate dynamics with respect to different input factors. To develop effective control strategies, the system's dynamical behavior is examined, and the influence of fractional derivative order on fluctuations is explored. This research offers a range of suggestions aimed at reducing the occurrence of social media addiction.<\/jats:p>","DOI":"10.3389\/fams.2023.1210404","type":"journal-article","created":{"date-parts":[[2023,8,9]],"date-time":"2023-08-09T12:24:05Z","timestamp":1691583845000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":11,"title":["Modeling and analysis of the addiction of social media through fractional calculus"],"prefix":"10.3389","volume":"9","author":[{"given":"Meshal","family":"Shutaywi","sequence":"first","affiliation":[]},{"given":"Ziad Ur","family":"Rehman","sequence":"additional","affiliation":[]},{"given":"Zahir","family":"Shah","sequence":"additional","affiliation":[]},{"given":"Narcisa","family":"Vrinceanu","sequence":"additional","affiliation":[]},{"given":"Rashid","family":"Jan","sequence":"additional","affiliation":[]},{"given":"Wejdan","family":"Deebani","sequence":"additional","affiliation":[]},{"given":"Oana","family":"Dumitrascu","sequence":"additional","affiliation":[]}],"member":"1965","published-online":{"date-parts":[[2023,8,9]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"160","DOI":"10.1556\/JBA.2.2013.006","article-title":"Psychological risk factors of addiction to social networking sites among Chinese smartphone users","volume":"2","author":"Wu","year":"2013","journal-title":"J Behav Addict."},{"key":"B2","first-page":"53","article-title":"Social media: usage and influence on undergraduate studies in Nigerian universities","volume":"15","author":"Tayo","year":"2019","journal-title":"Int J Educ Dev Inform Commun Technol."},{"key":"B3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.5935\/MedicalExpress.2016.01.01","article-title":"Social networking, a new online addiction: a review of Facebook and other addiction disorders","volume":"3","author":"Guedes","year":"2016","journal-title":"MedicalExpress"},{"key":"B4","doi-asserted-by":"publisher","first-page":"71","DOI":"10.7753\/IJCATR0502.1006","article-title":"Social media its impact with positive and negative aspects","volume":"5","author":"Siddiqui","year":"2016","journal-title":"Int J Comput Appl Technol Res."},{"key":"B5","doi-asserted-by":"publisher","first-page":"106","DOI":"10.30935\/cet.554452","article-title":"A comparative study on social media addiction of high school and university students","volume":"10","author":"Simsek","year":"2019","journal-title":"Contemp Educ Technol."},{"key":"B6","doi-asserted-by":"publisher","first-page":"13","DOI":"10.5817\/CP2019-1-4","article-title":"Social media addiction: its impact, mediation, and intervention","author":"Hou","year":"2019","journal-title":"Cyberpsychology"},{"key":"B7","doi-asserted-by":"publisher","first-page":"776","DOI":"10.1100\/tsw.2008.104","article-title":"Internet addiction in Chinese adolescents in Hong Kong: assessment, profiles, and psychosocial correlates","volume":"8","author":"Shek","year":"2008","journal-title":"The Scientific World Journal"},{"key":"B8","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1556\/2006.6.2017.023","article-title":"Social networking addiction, attachment style, and validation of the Italian version of the Bergen Social Media Addiction Scale","volume":"6","author":"Monacis","year":"2017","journal-title":"J Behav Addict."},{"key":"B9","first-page":"123","article-title":"Internet addiction: consensus, controversies, and the way ahead","volume":"20","author":"Chakraborty","year":"2010","journal-title":"East Asian Arch Psychiatry"},{"key":"B10","doi-asserted-by":"publisher","first-page":"4891601","DOI":"10.1155\/2022\/4891601","article-title":"Learning methods of business intelligence and group related diagnostics on patient management by using artificial dynamic system","volume":"2022","author":"Hamad","year":"2022","journal-title":"J Nanomater."},{"key":"B11","doi-asserted-by":"publisher","first-page":"2250036","DOI":"10.1142\/S179352452250036X","article-title":"Analysis and dynamical behavior of a novel dengue model via fractional calculus","volume":"15","author":"Jan","year":"2022","journal-title":"Int J Biomath."},{"key":"B12","doi-asserted-by":"publisher","first-page":"1526931","DOI":"10.1155\/2021\/1526931","article-title":"The commitment of Nineveh governorate residents to the precautionary measures against global 2019 pandemic and dermatological affection of precautions","volume":"2021","author":"Al-Rahawe","year":"2021","journal-title":"Appl Bionics Biomech."},{"key":"B13","volume-title":"Effect of Social Media on Academic Performance of Students in Ghanaian Universities: A Case Study of University of Ghana","author":"Bernard","year":"2018"},{"key":"B14","doi-asserted-by":"publisher","first-page":"705","DOI":"10.1515\/phys-2017-0083","article-title":"Lie algebraic discussion for affinity based information diffusion in social networks","volume":"15","author":"Shang","year":"2017","journal-title":"Open Phys."},{"key":"B15","doi-asserted-by":"publisher","first-page":"27","DOI":"10.5121\/ijait.2018.8503","article-title":"The impact of social media on academic performance of selected college students","volume":"8","author":"Al Rushaidan","year":"2018","journal-title":"Int J Adv Inform Technol."},{"key":"B16","doi-asserted-by":"publisher","first-page":"554","DOI":"10.1556\/2006.8.2019.49","article-title":"Strategies for self-controlling social media use: Classification and role in preventing social media addiction symptoms","volume":"8","author":"Brevers","year":"2019","journal-title":"J Behav Addict."},{"key":"B17","doi-asserted-by":"publisher","first-page":"8113760","DOI":"10.1155\/2022\/8113760","article-title":"Chaotic phenomena and oscillations in dynamical behaviour of financial system via fractional calculus","volume":"2022","author":"Shah","year":"2022","journal-title":"Complexity"},{"key":"B18","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1016\/j.amc.2014.11.028","article-title":"Diffusion process modeling by using fractional-order models","volume":"257","author":"Sierociuk","year":"2015","journal-title":"Appl Math Comput."},{"key":"B19","doi-asserted-by":"publisher","first-page":"3329","DOI":"10.1016\/j.camwa.2012.01.005","article-title":"The fractional-order modeling and synchronization of electrically coupled neuron systems","volume":"64","author":"Moaddy","year":"2012","journal-title":"Comput Math Appl."},{"key":"B20","volume-title":"Fractional integrals and derivatives","author":"Samko","year":"1993"},{"key":"B21","first-page":"73","article-title":"A new definition of fractional derivative without singular kernel","volume":"1","author":"Caputo","year":"2015","journal-title":"Prog Fract Different Appl."},{"key":"B22","first-page":"87","article-title":"Properties of a new fractional derivative without singular kernel","volume":"1","author":"Losada","year":"2015","journal-title":"Prog Fract Different Appl."},{"key":"B23","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1051\/mmnp\/2018010","article-title":"New numerical approach for fractional differential equations","volume":"13","author":"Atangana","year":"2018","journal-title":"Math Modell Nat Phenomena"}],"container-title":["Frontiers in Applied Mathematics and Statistics"],"original-title":[],"link":[{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fams.2023.1210404\/full","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,9]],"date-time":"2023-08-09T12:24:13Z","timestamp":1691583853000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fams.2023.1210404\/full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,9]]},"references-count":23,"alternative-id":["10.3389\/fams.2023.1210404"],"URL":"https:\/\/doi.org\/10.3389\/fams.2023.1210404","relation":{},"ISSN":["2297-4687"],"issn-type":[{"value":"2297-4687","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,9]]},"article-number":"1210404"}}