{"title":"奇异积分方程和非齐次抛物型偏微分方程的直接方法","authors":"A. Aghili","doi":"10.33993/jnaat512-1269","DOIUrl":null,"url":null,"abstract":"In this article, the author presented some applications of the Laplace, \\(L^2\\), and Post-Widder transforms for solving fractional Singular Integral Equations, impulsive differential equation and systems of differential equations. Finally, analytic solution for a non-homogeneous partial differential equation with non-constant coefficients is given. The obtained results reveal that the integral transform method is an effective tool and convenient.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"93 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Direct methods for singular integral equations and non-homogeneous parabolic PDEs\",\"authors\":\"A. Aghili\",\"doi\":\"10.33993/jnaat512-1269\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, the author presented some applications of the Laplace, \\\\(L^2\\\\), and Post-Widder transforms for solving fractional Singular Integral Equations, impulsive differential equation and systems of differential equations. Finally, analytic solution for a non-homogeneous partial differential equation with non-constant coefficients is given. The obtained results reveal that the integral transform method is an effective tool and convenient.\",\"PeriodicalId\":287022,\"journal\":{\"name\":\"Journal of Numerical Analysis and Approximation Theory\",\"volume\":\"93 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-12-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Numerical Analysis and Approximation Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33993/jnaat512-1269\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Numerical Analysis and Approximation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33993/jnaat512-1269","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Direct methods for singular integral equations and non-homogeneous parabolic PDEs
In this article, the author presented some applications of the Laplace, \(L^2\), and Post-Widder transforms for solving fractional Singular Integral Equations, impulsive differential equation and systems of differential equations. Finally, analytic solution for a non-homogeneous partial differential equation with non-constant coefficients is given. The obtained results reveal that the integral transform method is an effective tool and convenient.
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