{"title":"Applications of the Fractional Sturm–Liouville Difference Problem to the Fractional Diffusion Difference Equation","authors":"A. Malinowska, T. Odzijewicz, A. Poskrobko","doi":"10.34768/amcs-2023-0025","DOIUrl":null,"url":null,"abstract":"Abstract This paper deals with homogeneous and non-homogeneous fractional diffusion difference equations. The fractional operators in space and time are defined in the sense of Grünwald and Letnikov. Applying results on the existence of eigenvalues and corresponding eigenfunctions of the Sturm–Liouville problem, we show that solutions of fractional diffusion difference equations exist and are given by a finite series.","PeriodicalId":502322,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"38 1","pages":"349 - 359"},"PeriodicalIF":0.0000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Applied Mathematics and Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.34768/amcs-2023-0025","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract This paper deals with homogeneous and non-homogeneous fractional diffusion difference equations. The fractional operators in space and time are defined in the sense of Grünwald and Letnikov. Applying results on the existence of eigenvalues and corresponding eigenfunctions of the Sturm–Liouville problem, we show that solutions of fractional diffusion difference equations exist and are given by a finite series.
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