{"title":"Controllability Criteria for Nonlinear Impulsive Fractional Differential Systems with Distributed Delays in Controls","authors":"A. Debbouche, B. Vadivoo, V. Fedorov, V. Antonov","doi":"10.3390/mca28010013","DOIUrl":null,"url":null,"abstract":"We establish a class of nonlinear fractional differential systems with distributed time delays in the controls and impulse effects. We discuss the controllability criteria for both linear and nonlinear systems. The main results required a suitable Gramian matrix defined by the Mittag–Leffler function, using the standard Laplace transform and Schauder fixed-point techniques. Further, we provide an illustrative example supported by graphical representations to show the validity of the obtained abstract results.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2023-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical & Computational Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/mca28010013","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
We establish a class of nonlinear fractional differential systems with distributed time delays in the controls and impulse effects. We discuss the controllability criteria for both linear and nonlinear systems. The main results required a suitable Gramian matrix defined by the Mittag–Leffler function, using the standard Laplace transform and Schauder fixed-point techniques. Further, we provide an illustrative example supported by graphical representations to show the validity of the obtained abstract results.
期刊介绍：
Mathematical and Computational Applications (MCA) is devoted to original research in the field of engineering, natural sciences or social sciences where mathematical and/or computational techniques are necessary for solving specific problems. The aim of the journal is to provide a medium by which a wide range of experience can be exchanged among researchers from diverse fields such as engineering (electrical, mechanical, civil, industrial, aeronautical, nuclear etc.), natural sciences (physics, mathematics, chemistry, biology etc.) or social sciences (administrative sciences, economics, political sciences etc.). The papers may be theoretical where mathematics is used in a nontrivial way or computational or combination of both. Each paper submitted will be reviewed and only papers of highest quality that contain original ideas and research will be published. Papers containing only experimental techniques and abstract mathematics without any sign of application are discouraged.
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