{"title":"非局部随机微分算子混沌模型的理论与数值分析","authors":"I. Koca, A. Atangana","doi":"10.11121/ijocta.2023.1398","DOIUrl":null,"url":null,"abstract":"A set of nonlinear ordinary differential equations has been considered in this paper. The work tries to establish some theoretical and analytical insights when the usual time-deferential operator is replaced with the Caputo fractional derivative. Using the Caratheodory principle and other additional conditions, we established that the system has a unique system of solutions. A variety of well-known approaches were used to investigate the system. The stochastic version of this system was solved using a numerical approach based on Lagrange interpolation, and numerical simulation results were produced.","PeriodicalId":37369,"journal":{"name":"International Journal of Optimization and Control: Theories and Applications","volume":"104 1","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Theoretical and numerical analysis of a chaotic model with nonlocal and stochastic differential operators\",\"authors\":\"I. Koca, A. Atangana\",\"doi\":\"10.11121/ijocta.2023.1398\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A set of nonlinear ordinary differential equations has been considered in this paper. The work tries to establish some theoretical and analytical insights when the usual time-deferential operator is replaced with the Caputo fractional derivative. Using the Caratheodory principle and other additional conditions, we established that the system has a unique system of solutions. A variety of well-known approaches were used to investigate the system. The stochastic version of this system was solved using a numerical approach based on Lagrange interpolation, and numerical simulation results were produced.\",\"PeriodicalId\":37369,\"journal\":{\"name\":\"International Journal of Optimization and Control: Theories and Applications\",\"volume\":\"104 1\",\"pages\":\"\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2023-07-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Optimization and Control: Theories and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.11121/ijocta.2023.1398\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Optimization and Control: Theories and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11121/ijocta.2023.1398","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Theoretical and numerical analysis of a chaotic model with nonlocal and stochastic differential operators
A set of nonlinear ordinary differential equations has been considered in this paper. The work tries to establish some theoretical and analytical insights when the usual time-deferential operator is replaced with the Caputo fractional derivative. Using the Caratheodory principle and other additional conditions, we established that the system has a unique system of solutions. A variety of well-known approaches were used to investigate the system. The stochastic version of this system was solved using a numerical approach based on Lagrange interpolation, and numerical simulation results were produced.