{"title":"奇摄动积分-微分系统中快速振荡非均匀性对附加边界层形成的影响","authors":"M. Akylbayev, Burhan Kali̇mbetov, N. Pardaeva","doi":"10.31197/atnaa.1264072","DOIUrl":null,"url":null,"abstract":"In this paper, the Lomov's regularization method is generalized to a singularly perturbed integro-differential equation with a fractional derivative and with a rapidly oscillating inhomogeneity. The main goal of the work is to reveal the influence of a rapidly changing kernel on the structure of the asymptotics of the problem solution and to study additional boundary functions that are generated by rapidly oscillating inhomogeneities.","PeriodicalId":7440,"journal":{"name":"Advances in the Theory of Nonlinear Analysis and its Application","volume":"158 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Influence of rapidly oscillating inhomogeneities in the formation of additional boundary layers for singularly perturbed integro-differential systems\",\"authors\":\"M. Akylbayev, Burhan Kali̇mbetov, N. Pardaeva\",\"doi\":\"10.31197/atnaa.1264072\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, the Lomov's regularization method is generalized to a singularly perturbed integro-differential equation with a fractional derivative and with a rapidly oscillating inhomogeneity. The main goal of the work is to reveal the influence of a rapidly changing kernel on the structure of the asymptotics of the problem solution and to study additional boundary functions that are generated by rapidly oscillating inhomogeneities.\",\"PeriodicalId\":7440,\"journal\":{\"name\":\"Advances in the Theory of Nonlinear Analysis and its Application\",\"volume\":\"158 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-06-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in the Theory of Nonlinear Analysis and its Application\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31197/atnaa.1264072\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in the Theory of Nonlinear Analysis and its Application","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31197/atnaa.1264072","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Influence of rapidly oscillating inhomogeneities in the formation of additional boundary layers for singularly perturbed integro-differential systems
In this paper, the Lomov's regularization method is generalized to a singularly perturbed integro-differential equation with a fractional derivative and with a rapidly oscillating inhomogeneity. The main goal of the work is to reveal the influence of a rapidly changing kernel on the structure of the asymptotics of the problem solution and to study additional boundary functions that are generated by rapidly oscillating inhomogeneities.
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