The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design
The paper presents the mathematical dynamics and numerical simulations for a fractional-order social media addiction (FSMA) model. This addiction structure is replaced by involving the Caputo fractional (CF) derivative to get the FSMA model. In this study, our main goal is to understand how the frac...
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| Format: | Article |
| Language: | English |
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Emrah Evren KARA
2025-03-01
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| Series: | Communications in Advanced Mathematical Sciences |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/4257090 |
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| author | Emrah Karaman Bahar Karaman |
| author_facet | Emrah Karaman Bahar Karaman |
| author_sort | Emrah Karaman |
| collection | DOAJ |
| description | The paper presents the mathematical dynamics and numerical simulations for a fractional-order social media addiction (FSMA) model. This addiction structure is replaced by involving the Caputo fractional (CF) derivative to get the FSMA model. In this study, our main goal is to understand how the fractional derivative impresses the dynamics of the model. Thus, the theoretical properties are first examined. Afterward, the stability properties of the mentioned model are discussed. Besides, the fractional backward differentiation formula (FBDF) displays numerical simulations of the model. Observing both theoretical and numerical results, the two equilibrium points' stability is not impacted by the order of fractional derivatives. However, each solution converges more quickly to its stationary state for higher values of the fractional-order derivative. Finally, we would like to say that the acquired numerical results are compatible with our theoretical outcomes. |
| format | Article |
| id | doaj-art-313df20d0a4b48e1a0c2f34f0385f6d3 |
| institution | Kabale University |
| issn | 2651-4001 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Communications in Advanced Mathematical Sciences |
| spelling | doaj-art-313df20d0a4b48e1a0c2f34f0385f6d32025-08-20T03:51:59ZengEmrah Evren KARACommunications in Advanced Mathematical Sciences2651-40012025-03-018111010.33434/cams.15598081225The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction DesignEmrah Karaman0https://orcid.org/0000-0002-0466-3827Bahar Karaman1https://orcid.org/0000-0001-6631-8562ESKİŞEHİR TEKNİK ÜNİVERSİTESİ, FEN FAKÜLTESİ, MATEMATİK BÖLÜMÜESKİŞEHİR TEKNİK ÜNİVERSİTESİ, FEN FAKÜLTESİ, MATEMATİK BÖLÜMÜThe paper presents the mathematical dynamics and numerical simulations for a fractional-order social media addiction (FSMA) model. This addiction structure is replaced by involving the Caputo fractional (CF) derivative to get the FSMA model. In this study, our main goal is to understand how the fractional derivative impresses the dynamics of the model. Thus, the theoretical properties are first examined. Afterward, the stability properties of the mentioned model are discussed. Besides, the fractional backward differentiation formula (FBDF) displays numerical simulations of the model. Observing both theoretical and numerical results, the two equilibrium points' stability is not impacted by the order of fractional derivatives. However, each solution converges more quickly to its stationary state for higher values of the fractional-order derivative. Finally, we would like to say that the acquired numerical results are compatible with our theoretical outcomes.https://dergipark.org.tr/en/download/article-file/4257090fractional backward differentiation formula(fbdf)social media addictionstability analysis |
| spellingShingle | Emrah Karaman Bahar Karaman The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design Communications in Advanced Mathematical Sciences fractional backward differentiation formula(fbdf) social media addiction stability analysis |
| title | The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design |
| title_full | The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design |
| title_fullStr | The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design |
| title_full_unstemmed | The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design |
| title_short | The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design |
| title_sort | mathematical dynamics of the caputo fractional order social media addiction design |
| topic | fractional backward differentiation formula(fbdf) social media addiction stability analysis |
| url | https://dergipark.org.tr/en/download/article-file/4257090 |
| work_keys_str_mv | AT emrahkaraman themathematicaldynamicsofthecaputofractionalordersocialmediaaddictiondesign AT baharkaraman themathematicaldynamicsofthecaputofractionalordersocialmediaaddictiondesign AT emrahkaraman mathematicaldynamicsofthecaputofractionalordersocialmediaaddictiondesign AT baharkaraman mathematicaldynamicsofthecaputofractionalordersocialmediaaddictiondesign |