{"title":"Semi-analytical approximation of time-fractional telegraph equation via natural transform in Caputo derivative","authors":"Mamta Kapoor, Samanyu Khosla","doi":"10.1515/nleng-2022-0289","DOIUrl":null,"url":null,"abstract":"Abstract In the present research study, time-fractional hyperbolic telegraph equations are solved iteratively using natural transform in one, two, and three dimensions. The fractional derivative is considered in the Caputo sense. These equations serve as a model for the wave theory process of signal processing and transmission of electric impulses. To evaluate the validity and effectiveness of the suggested strategy, a graphical comparison of approximated and exact findings is performed. Convergence analysis of the approximations utilising L ∞ {L}_{\\infty } has been done using tables. The suggested approach may successfully and without errors solve a wide variety of ordinary differential equations, partial differential equations (PDEs), fractional PDEs, and fractional hyperbolic telegraph equations. Graphical abstract","PeriodicalId":37863,"journal":{"name":"Nonlinear Engineering - Modeling and Application","volume":"216 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Engineering - Modeling and Application","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/nleng-2022-0289","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 2
Abstract
Abstract In the present research study, time-fractional hyperbolic telegraph equations are solved iteratively using natural transform in one, two, and three dimensions. The fractional derivative is considered in the Caputo sense. These equations serve as a model for the wave theory process of signal processing and transmission of electric impulses. To evaluate the validity and effectiveness of the suggested strategy, a graphical comparison of approximated and exact findings is performed. Convergence analysis of the approximations utilising L ∞ {L}_{\infty } has been done using tables. The suggested approach may successfully and without errors solve a wide variety of ordinary differential equations, partial differential equations (PDEs), fractional PDEs, and fractional hyperbolic telegraph equations. Graphical abstract
期刊介绍：
The Journal of Nonlinear Engineering aims to be a platform for sharing original research results in theoretical, experimental, practical, and applied nonlinear phenomena within engineering. It serves as a forum to exchange ideas and applications of nonlinear problems across various engineering disciplines. Articles are considered for publication if they explore nonlinearities in engineering systems, offering realistic mathematical modeling, utilizing nonlinearity for new designs, stabilizing systems, understanding system behavior through nonlinearity, optimizing systems based on nonlinear interactions, and developing algorithms to harness and leverage nonlinear elements.
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