Studying the Dynamics of the Rumor Spread Model with Fractional Piecewise Derivative
Sensitively altered news, commonly referred to as rumors, can lead an individual, organization, or nation astray, potentially resulting in harm, even to the extent of causing violence among large groups of people. In this digital age, news can be easily twisted and rapidly spread through the interne...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/15/8/1537 |
| _version_ | 1797583142387712000 |
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| author | Badr Saad T. Alkahtani Sara Salem Alzaid |
| author_facet | Badr Saad T. Alkahtani Sara Salem Alzaid |
| author_sort | Badr Saad T. Alkahtani |
| collection | DOAJ |
| description | Sensitively altered news, commonly referred to as rumors, can lead an individual, organization, or nation astray, potentially resulting in harm, even to the extent of causing violence among large groups of people. In this digital age, news can be easily twisted and rapidly spread through the internet and social media. It becomes challenging for consumers to discern whether the information they encounter online has been manipulated. Unfortunately, the rise of internet forgeries has facilitated the dissemination of false or distorted information by unscrupulous individuals, particularly on sensitive matters, to serve their own interests. Once a rumor is generated and made public on the internet, it quickly spreads through sharing and discussions by anonymous individuals, sometimes intentionally, without thorough fact-checking. In this manuscript, we investigate the dynamical model of rumor propagation in a social network using the classical Caputo piecewise derivative. We examine the existence and uniqueness of a solution for the aforementioned problem and analyze the equilibrium, stability, boundedness, and positivity of the model. To obtain the numerical simulation of the piecewise derivative, we employ various fractional orders, and the approximate solution of the considered model is found using the fractional piecewise numerical iterative approach of the Newton polynomial. This approach allows us to gain valuable insights into the dynamics of rumor propagation and its effects within a social network. |
| first_indexed | 2024-03-10T23:32:38Z |
| format | Article |
| id | doaj.art-6b8eda5978184711b8bc919f7b595c60 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T23:32:38Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-6b8eda5978184711b8bc919f7b595c602023-11-19T03:11:10ZengMDPI AGSymmetry2073-89942023-08-01158153710.3390/sym15081537Studying the Dynamics of the Rumor Spread Model with Fractional Piecewise DerivativeBadr Saad T. Alkahtani0Sara Salem Alzaid1Department of Mathematics, College of Science, King Saud University, P.O. Box 1142, Riyadh 11989, Saudi ArabiaDepartment of Mathematics, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaSensitively altered news, commonly referred to as rumors, can lead an individual, organization, or nation astray, potentially resulting in harm, even to the extent of causing violence among large groups of people. In this digital age, news can be easily twisted and rapidly spread through the internet and social media. It becomes challenging for consumers to discern whether the information they encounter online has been manipulated. Unfortunately, the rise of internet forgeries has facilitated the dissemination of false or distorted information by unscrupulous individuals, particularly on sensitive matters, to serve their own interests. Once a rumor is generated and made public on the internet, it quickly spreads through sharing and discussions by anonymous individuals, sometimes intentionally, without thorough fact-checking. In this manuscript, we investigate the dynamical model of rumor propagation in a social network using the classical Caputo piecewise derivative. We examine the existence and uniqueness of a solution for the aforementioned problem and analyze the equilibrium, stability, boundedness, and positivity of the model. To obtain the numerical simulation of the piecewise derivative, we employ various fractional orders, and the approximate solution of the considered model is found using the fractional piecewise numerical iterative approach of the Newton polynomial. This approach allows us to gain valuable insights into the dynamics of rumor propagation and its effects within a social network.https://www.mdpi.com/2073-8994/15/8/1537rumor spread modelpiecewise derivativeclassical derivativeCaputo operator |
| spellingShingle | Badr Saad T. Alkahtani Sara Salem Alzaid Studying the Dynamics of the Rumor Spread Model with Fractional Piecewise Derivative Symmetry rumor spread model piecewise derivative classical derivative Caputo operator |
| title | Studying the Dynamics of the Rumor Spread Model with Fractional Piecewise Derivative |
| title_full | Studying the Dynamics of the Rumor Spread Model with Fractional Piecewise Derivative |
| title_fullStr | Studying the Dynamics of the Rumor Spread Model with Fractional Piecewise Derivative |
| title_full_unstemmed | Studying the Dynamics of the Rumor Spread Model with Fractional Piecewise Derivative |
| title_short | Studying the Dynamics of the Rumor Spread Model with Fractional Piecewise Derivative |
| title_sort | studying the dynamics of the rumor spread model with fractional piecewise derivative |
| topic | rumor spread model piecewise derivative classical derivative Caputo operator |
| url | https://www.mdpi.com/2073-8994/15/8/1537 |
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