{"title":"An efficient technique for solving fractional diffusion equations arising in oil pollution via natural transform","authors":"Lalit Mohan, Amit Prakash","doi":"10.1080/17455030.2023.2273323","DOIUrl":null,"url":null,"abstract":"AbstractIn this paper, we consider the time-fractional non-linear diffusion equations for describing the pollution caused by oil in the water. The hybrid computational technique, the Natural Transform Homotopy Perturbation Technique is applied to get a numerical solution to the time-fractional non-linear diffusion equation. The existence and uniqueness are analyzed with the help of the fixed point theorem, also the stability analysis is discussed by using the Lyapunov function.KEYWORDS: Fractional diffusion equationCaputo derivativeLyapunov functionnatural transformhomotopy perturbation transform techniquefixed point theorem Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":23598,"journal":{"name":"Waves in Random and Complex Media","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Waves in Random and Complex Media","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/17455030.2023.2273323","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
AbstractIn this paper, we consider the time-fractional non-linear diffusion equations for describing the pollution caused by oil in the water. The hybrid computational technique, the Natural Transform Homotopy Perturbation Technique is applied to get a numerical solution to the time-fractional non-linear diffusion equation. The existence and uniqueness are analyzed with the help of the fixed point theorem, also the stability analysis is discussed by using the Lyapunov function.KEYWORDS: Fractional diffusion equationCaputo derivativeLyapunov functionnatural transformhomotopy perturbation transform techniquefixed point theorem Disclosure statementNo potential conflict of interest was reported by the author(s).
期刊介绍：
Waves in Random and Complex Media (formerly Waves in Random Media ) is a broad, interdisciplinary journal that reports theoretical, applied and experimental research related to any wave phenomena.
The field of wave phenomena is all-pervading, fast-moving and exciting; more and more, researchers are looking for a journal which addresses the understanding of wave-matter interactions in increasingly complex natural and engineered media. With its foundations in the scattering and propagation community, Waves in Random and Complex Media is becoming a key forum for research in both established fields such as imaging through turbulence, as well as emerging fields such as metamaterials.
The Journal is of interest to scientists and engineers working in the field of wave propagation, scattering and imaging in random or complex media. Papers on theoretical developments, experimental results and analytical/numerical studies are considered for publication, as are deterministic problems when also linked to random or complex media. Papers are expected to report original work, and must be comprehensible and of general interest to the broad community working with wave phenomena.
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