Hassan Tahir, Anwarud Din, Kamal Shah, Maggie Aphane, Thabet Abdeljawad
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This article discusses a fractional <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_phys-2023-0190_eq_001.png\" /> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"sans-serif\">S</m:mi> <m:msub> <m:mrow> <m:mi mathvariant=\"sans-serif\">E</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mi mathvariant=\"sans-serif\">E</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> <m:mi mathvariant=\"sans-serif\">I</m:mi> <m:mi mathvariant=\"sans-serif\">R</m:mi> </m:math> <jats:tex-math>{\\mathsf{S}}{{\\mathsf{E}}}_{1}{{\\mathsf{E}}}_{2}{\\mathsf{I}}{\\mathsf{R}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> model to explain worm propagation in WSNs. For capturing the dynamics of the virus, we use the Mittag–Leffler kernel and the Atangana–Baleanu (AB) Caputo operator. Besides other characteristics of the problem, the properties of superposition and Lipschitzness of the AB Caputo derivatives are studied. Standard numerical methods were employed to approximate the Atangana–Baleanu–Caputto fractional derivative, and a detailed analysis is presented. To illustrate our analytical conclusions, we ran numerical simulations.","PeriodicalId":48710,"journal":{"name":"Open Physics","volume":"2016 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dynamic properties of the multimalware attacks in wireless sensor networks: Fractional derivative analysis of wireless sensor networks\",\"authors\":\"Hassan Tahir, Anwarud Din, Kamal Shah, Maggie Aphane, Thabet Abdeljawad\",\"doi\":\"10.1515/phys-2023-0190\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Due to inherent operating constraints, wireless sensor networks (WSNs) need help assuring network security. This problem is caused by worms entering the networks, which can spread uncontrollably to nearby nodes from a single node infected with computer viruses, worms, trojans, and other malicious software, which can compromise the network’s integrity and functionality. This article discusses a fractional <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_phys-2023-0190_eq_001.png\\\" /> <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\"> <m:mi mathvariant=\\\"sans-serif\\\">S</m:mi> <m:msub> <m:mrow> <m:mi mathvariant=\\\"sans-serif\\\">E</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mi mathvariant=\\\"sans-serif\\\">E</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> <m:mi mathvariant=\\\"sans-serif\\\">I</m:mi> <m:mi mathvariant=\\\"sans-serif\\\">R</m:mi> </m:math> <jats:tex-math>{\\\\mathsf{S}}{{\\\\mathsf{E}}}_{1}{{\\\\mathsf{E}}}_{2}{\\\\mathsf{I}}{\\\\mathsf{R}}</jats:tex-math> </jats:alternatives> </jats:inline-formula> model to explain worm propagation in WSNs. For capturing the dynamics of the virus, we use the Mittag–Leffler kernel and the Atangana–Baleanu (AB) Caputo operator. Besides other characteristics of the problem, the properties of superposition and Lipschitzness of the AB Caputo derivatives are studied. Standard numerical methods were employed to approximate the Atangana–Baleanu–Caputto fractional derivative, and a detailed analysis is presented. 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引用次数: 0
摘要
由于固有的运行限制,无线传感器网络(WSN)需要帮助确保网络安全。造成这一问题的原因是蠕虫进入网络,感染计算机病毒、蠕虫、木马和其他恶意软件的单个节点会不受控制地向附近的节点传播,从而破坏网络的完整性和功能。本文讨论了一个分数 S E 1 E 2 I R {mathsf{S}}{{\mathsf{E}}_{1}{{mathsf{E}}_{2}{mathsf{I}}{mathsf{R}} 模型来解释 WSN 中的蠕虫传播。为了捕捉病毒的动态变化,我们使用了 Mittag-Leffler 核和 Atangana-Baleanu (AB) Caputo 算子。除了问题的其他特征外,我们还研究了 AB 卡普托导数的叠加和 Lipschitzness 特性。采用标准数值方法对阿坦加纳-巴莱阿努-卡普托分数导数进行了近似,并给出了详细分析。为了说明我们的分析结论,我们进行了数值模拟。
Dynamic properties of the multimalware attacks in wireless sensor networks: Fractional derivative analysis of wireless sensor networks
Due to inherent operating constraints, wireless sensor networks (WSNs) need help assuring network security. This problem is caused by worms entering the networks, which can spread uncontrollably to nearby nodes from a single node infected with computer viruses, worms, trojans, and other malicious software, which can compromise the network’s integrity and functionality. This article discusses a fractional SE1E2IR{\mathsf{S}}{{\mathsf{E}}}_{1}{{\mathsf{E}}}_{2}{\mathsf{I}}{\mathsf{R}} model to explain worm propagation in WSNs. For capturing the dynamics of the virus, we use the Mittag–Leffler kernel and the Atangana–Baleanu (AB) Caputo operator. Besides other characteristics of the problem, the properties of superposition and Lipschitzness of the AB Caputo derivatives are studied. Standard numerical methods were employed to approximate the Atangana–Baleanu–Caputto fractional derivative, and a detailed analysis is presented. To illustrate our analytical conclusions, we ran numerical simulations.
期刊介绍:
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