{"title":"Computational solution of fractional pantograph equation with varying delay term","authors":"M. Khalid, S. K. Fareeha, S. Mariam","doi":"10.4310/amsa.2021.v6.n2.a1","DOIUrl":null,"url":null,"abstract":"Delay Differential Equations DDEs have great importance in real life phenomena. Among them is a special type of equation known as Pantograph Delay Differential Equation PDDE. Such kind of equations cannot be solved using ordinary methods, and hence, it becomes a challenge when the complexity increases, especially if one wants to study Fractional Pantograph Delay Differential Equation (FPDDE). In this work, FPDDEs with a general Delay term is solved numerically by an iteration method called Perturbation Iteration Algorithm (PIA). It is based on the Taylor series and elim-inates the non-linear terms easily. Iterative results are discussed in detail in both tabular and graphical forms. A graphical interpre-tation of the variability of the Delay term is also provided for a deeper understanding of its range.","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Mathematical Sciences and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/amsa.2021.v6.n2.a1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
Delay Differential Equations DDEs have great importance in real life phenomena. Among them is a special type of equation known as Pantograph Delay Differential Equation PDDE. Such kind of equations cannot be solved using ordinary methods, and hence, it becomes a challenge when the complexity increases, especially if one wants to study Fractional Pantograph Delay Differential Equation (FPDDE). In this work, FPDDEs with a general Delay term is solved numerically by an iteration method called Perturbation Iteration Algorithm (PIA). It is based on the Taylor series and elim-inates the non-linear terms easily. Iterative results are discussed in detail in both tabular and graphical forms. A graphical interpre-tation of the variability of the Delay term is also provided for a deeper understanding of its range.