Meriem Mansouria BELHAMITI, Zoubir DAHMANİ, Mehmet Zeki SARIKAYA
{"title":"具有新混沌动力学的两分数阶朗之万方程","authors":"Meriem Mansouria BELHAMITI, Zoubir DAHMANİ, Mehmet Zeki SARIKAYA","doi":"10.31801/cfsuasmas.1126025","DOIUrl":null,"url":null,"abstract":"In the present paper, we introduce a two-order nonlinear fractional sequential Langevin equation using the derivatives of Atangana-Baleanu and Caputo-Fabrizio. The existence of solutions is proven using a fixed point theorem under a weak topology, and an illustrative example is then given. Furthermore, we present new fractional versions of the Adams-Bashforth three-step approach for the Atangana-Baleanu and Caputo derivatives. New nonlinear chaotic dynamics are performed by numerical simulations.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":"11 1","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Two fractional order Langevin equation with new chaotic dynamics\",\"authors\":\"Meriem Mansouria BELHAMITI, Zoubir DAHMANİ, Mehmet Zeki SARIKAYA\",\"doi\":\"10.31801/cfsuasmas.1126025\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the present paper, we introduce a two-order nonlinear fractional sequential Langevin equation using the derivatives of Atangana-Baleanu and Caputo-Fabrizio. The existence of solutions is proven using a fixed point theorem under a weak topology, and an illustrative example is then given. Furthermore, we present new fractional versions of the Adams-Bashforth three-step approach for the Atangana-Baleanu and Caputo derivatives. New nonlinear chaotic dynamics are performed by numerical simulations.\",\"PeriodicalId\":44692,\"journal\":{\"name\":\"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics\",\"volume\":\"11 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-01-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31801/cfsuasmas.1126025\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31801/cfsuasmas.1126025","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Two fractional order Langevin equation with new chaotic dynamics
In the present paper, we introduce a two-order nonlinear fractional sequential Langevin equation using the derivatives of Atangana-Baleanu and Caputo-Fabrizio. The existence of solutions is proven using a fixed point theorem under a weak topology, and an illustrative example is then given. Furthermore, we present new fractional versions of the Adams-Bashforth three-step approach for the Atangana-Baleanu and Caputo derivatives. New nonlinear chaotic dynamics are performed by numerical simulations.
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