{"title":"求解弱奇异分式积分微分方程的新方法","authors":"Ali Jalal Ali, Mostafa Eslami, Ali Tavakoli","doi":"10.1016/j.padiff.2024.100922","DOIUrl":null,"url":null,"abstract":"<div><p>In this essay, we introduce a novel idea to tackle the challenges of fractional integro-differential equations (FIDEs) featuring weakly singular kernels (WSKs). New idea leverages B-splines for solving such equations, offering a robust numerical solution technique. We delve into the operational matrices integral to this method, providing comprehensive insights into their functionality. Furthermore, we establish the convergence of our approach and substantiate its effectiveness through various numerical examples.</p></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100922"},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666818124003085/pdfft?md5=993d5ac7cae4b379852574ce6443e170&pid=1-s2.0-S2666818124003085-main.pdf","citationCount":"0","resultStr":"{\"title\":\"A novel approach for solving weakly singular fractional integro-differential equations\",\"authors\":\"Ali Jalal Ali, Mostafa Eslami, Ali Tavakoli\",\"doi\":\"10.1016/j.padiff.2024.100922\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this essay, we introduce a novel idea to tackle the challenges of fractional integro-differential equations (FIDEs) featuring weakly singular kernels (WSKs). New idea leverages B-splines for solving such equations, offering a robust numerical solution technique. We delve into the operational matrices integral to this method, providing comprehensive insights into their functionality. Furthermore, we establish the convergence of our approach and substantiate its effectiveness through various numerical examples.</p></div>\",\"PeriodicalId\":34531,\"journal\":{\"name\":\"Partial Differential Equations in Applied Mathematics\",\"volume\":\"12 \",\"pages\":\"Article 100922\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S2666818124003085/pdfft?md5=993d5ac7cae4b379852574ce6443e170&pid=1-s2.0-S2666818124003085-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Partial Differential Equations in Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2666818124003085\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Partial Differential Equations in Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666818124003085","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
A novel approach for solving weakly singular fractional integro-differential equations
In this essay, we introduce a novel idea to tackle the challenges of fractional integro-differential equations (FIDEs) featuring weakly singular kernels (WSKs). New idea leverages B-splines for solving such equations, offering a robust numerical solution technique. We delve into the operational matrices integral to this method, providing comprehensive insights into their functionality. Furthermore, we establish the convergence of our approach and substantiate its effectiveness through various numerical examples.