{"title":"Generalized Laplace transform and tempered ψ-Caputo fractional derivative","authors":"M. Medved', M. Pospíšil","doi":"10.3846/mma.2023.16370","DOIUrl":null,"url":null,"abstract":"In this paper, images of the tempered Ψ-Hilfer fractional integral and the tempered Ψ-Caputo fractional derivative under the generalized Laplace transform are derived. The results are applied to find a solution to an initial value problem for a nonhomogeneous linear fractional differential equation with the tempered Ψ-Caputo fractional derivative of an order α for n− 1 <α<n N. An illustrative example is given for 0 <α<1 comparing solutions to the same initial value problem but with different tempering and Ψ.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2023-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Modelling and Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3846/mma.2023.16370","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
Abstract
In this paper, images of the tempered Ψ-Hilfer fractional integral and the tempered Ψ-Caputo fractional derivative under the generalized Laplace transform are derived. The results are applied to find a solution to an initial value problem for a nonhomogeneous linear fractional differential equation with the tempered Ψ-Caputo fractional derivative of an order α for n− 1 <α
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