Department of Mathematics, JECRC University, Jaipur 303905, Rajasthan, India.
Chaos. 2019 Jan;29(1):013137. doi: 10.1063/1.5080691.
Rumor plays a key role in social interaction, and its spreading has a notable influence on human lives. In this work, we study the rumor spreading dynamical model in a social network associated with the Atangana-Baleanu derivative of non-integer order. A deterministic model of the rumor spreading is studied. The solution of the rumor spreading dynamical model is obtained by employing an iterative scheme. Additionally, existence and uniqueness of the solution are discussed by employing the Picard-Lindelöf scheme. The effect of the order of AB fractional derivative on ignorants, spreaders, and stiflers is analyzed. Finally, to represent the obtained results, some numerical simulations are shown via graphs.
谣言在社交互动中扮演着关键的角色，其传播对人类生活有着显著的影响。在这项工作中，我们研究了与非整数阶 Atangana-Baleanu 导数相关的社交网络中的谣言传播动态模型。研究了谣言传播的确定性模型。通过迭代方案得到了谣言传播动力学模型的解。此外，通过 Picard-Lindelöf 方案讨论了解的存在唯一性。分析了 AB 分数阶导数的阶数对无知者、传播者和扼杀者的影响。最后，通过图形展示了一些数值模拟来表示所得到的结果。
