{"title":"变阶$q$-Hilfer分数阶混合积分-差分方程连续解的唯一性","authors":"Idris Ahmed, Norravich Limpanukorn, M. J. Ibrahim","doi":"10.48185/jmam.v2i3.421","DOIUrl":null,"url":null,"abstract":"In this paper, the authors introduced a novel definition based on Hilfer fractional derivative, which name $q$-Hilfer fractional derivative of variable order. And the uniqueness of solution to $q$-Hilfer fractional hybrid integro-difference equation of variable order of the form \\eqref{eq:varorderfrac} with $0 < \\alpha(t) < 1$, $0 \\leq \\beta \\leq 1$, and $0 < q < 1$ is studied. Moreover, an example is provided to demonstrate the result.","PeriodicalId":393347,"journal":{"name":"Journal of Mathematical Analysis and Modeling","volume":"44 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Uniqueness of continuous solution to $q$-Hilfer fractional hybrid integro-difference equation of variable order\",\"authors\":\"Idris Ahmed, Norravich Limpanukorn, M. J. Ibrahim\",\"doi\":\"10.48185/jmam.v2i3.421\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, the authors introduced a novel definition based on Hilfer fractional derivative, which name $q$-Hilfer fractional derivative of variable order. And the uniqueness of solution to $q$-Hilfer fractional hybrid integro-difference equation of variable order of the form \\\\eqref{eq:varorderfrac} with $0 < \\\\alpha(t) < 1$, $0 \\\\leq \\\\beta \\\\leq 1$, and $0 < q < 1$ is studied. Moreover, an example is provided to demonstrate the result.\",\"PeriodicalId\":393347,\"journal\":{\"name\":\"Journal of Mathematical Analysis and Modeling\",\"volume\":\"44 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-12-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Analysis and Modeling\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48185/jmam.v2i3.421\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Modeling","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48185/jmam.v2i3.421","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Uniqueness of continuous solution to $q$-Hilfer fractional hybrid integro-difference equation of variable order
In this paper, the authors introduced a novel definition based on Hilfer fractional derivative, which name $q$-Hilfer fractional derivative of variable order. And the uniqueness of solution to $q$-Hilfer fractional hybrid integro-difference equation of variable order of the form \eqref{eq:varorderfrac} with $0 < \alpha(t) < 1$, $0 \leq \beta \leq 1$, and $0 < q < 1$ is studied. Moreover, an example is provided to demonstrate the result.