The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design

Bahar Karaman; Emrah Karaman

doi:10.33434/cams.1559808

EN

The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design

Abstract

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.

Keywords

Fractional backward differentiation formula(FBDF), Social media addiction, Stability analysis

References

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Details

Primary Language

English

Subjects

Ordinary Differential Equations, Difference Equations and Dynamical Systems, Applied Mathematics (Other)

Journal Section

Research Article

Authors

Bahar Karaman ^*
0000-0001-6631-8562
Türkiye

Emrah Karaman
0000-0002-0466-3827
Türkiye

Early Pub Date

February 25, 2025

Publication Date

March 27, 2025

Submission Date

October 2, 2024

Acceptance Date

January 31, 2025

Published in Issue

Year 2025 Volume: 8 Number: 1

DOI

https://doi.org/10.33434/cams.1559808

IZ

https://izlik.org/JA34SS53LA

APA

Karaman, B., & Karaman, E. (2025). The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design. Communications in Advanced Mathematical Sciences, 8(1), 1-10. https://doi.org/10.33434/cams.1559808

AMA

1.Karaman B, Karaman E. The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design. Communications in Advanced Mathematical Sciences. 2025;8(1):1-10. doi:10.33434/cams.1559808

Chicago

Karaman, Bahar, and Emrah Karaman. 2025. “The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design”. Communications in Advanced Mathematical Sciences 8 (1): 1-10. https://doi.org/10.33434/cams.1559808.

EndNote

Karaman B, Karaman E (March 1, 2025) The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design. Communications in Advanced Mathematical Sciences 8 1 1–10.

IEEE

[1]B. Karaman and E. Karaman, “The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design”, Communications in Advanced Mathematical Sciences, vol. 8, no. 1, pp. 1–10, Mar. 2025, doi: 10.33434/cams.1559808.

ISNAD

Karaman, Bahar - Karaman, Emrah. “The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design”. Communications in Advanced Mathematical Sciences 8/1 (March 1, 2025): 1-10. https://doi.org/10.33434/cams.1559808.

JAMA

1.Karaman B, Karaman E. The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design. Communications in Advanced Mathematical Sciences. 2025;8:1–10.

MLA

Karaman, Bahar, and Emrah Karaman. “The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design”. Communications in Advanced Mathematical Sciences, vol. 8, no. 1, Mar. 2025, pp. 1-10, doi:10.33434/cams.1559808.

Vancouver

1.Bahar Karaman, Emrah Karaman. The Mathematical Dynamics of the Caputo Fractional Order Social Media Addiction Design. Communications in Advanced Mathematical Sciences. 2025 Mar. 1;8(1):1-10. doi:10.33434/cams.1559808

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Mathematical Sciences and Applications E-Notes

https://doi.org/10.36753/mathenot.1695610

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