{"title":"Theory of Hybrid Fractional Differential Equations with Complex Order","authors":"D. Vivek, O. Baghani, K. Kanagarajan","doi":"10.22130/SCMA.2018.72907.295","DOIUrl":null,"url":null,"abstract":"We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the existence of mild solutions of initial value problems for hybrid fractional differential equations. Finally, an application to solve one-variable linear fractional Schr\"odinger equation with complex order is given.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"15 1","pages":"65-76"},"PeriodicalIF":0.0000,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22130/SCMA.2018.72907.295","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 5
Abstract
We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0
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