Mokhtar Mokhtari, Ahmed Refice, M. S. Souid, A. Yakar
{"title":"On Weighted Cauchy-Type Problem of Riemann-Liouville Fractional Differential Equations in Lebesgue Spaces with Variable Exponent","authors":"Mokhtar Mokhtari, Ahmed Refice, M. S. Souid, A. Yakar","doi":"10.32323/ujma.1409291","DOIUrl":"https://doi.org/10.32323/ujma.1409291","url":null,"abstract":"This paper aims to investigate the existence, uniqueness, and stability properties for a class of fractional weighted Cauchy-type problem in the variable exponent Lebesgue space $L^{p(.)}$. The obtained results are set up by employing generalized intervals and piece-wise constant functions so that the $L^{p(.)}$ is transformed into the classical Lebesgue spaces.\u0000Moreover, the usual Banach Contraction Principle is utilized, and the Ulam-Hyers (UH) stability is studied. At the final stage, we provide an example to support the accuracy of the obtained results.","PeriodicalId":509012,"journal":{"name":"Universal Journal of Mathematics and Applications","volume":"12 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141021994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}