{"title":"卡普托导数下偏中性函数分微分方程的存在性和唯一性研究","authors":"N. Sene, A. Ndiaye","doi":"10.11121/ijocta.1464","DOIUrl":null,"url":null,"abstract":"The partial neutral functional fractional differential equation described by the fractional operator is considered in the present investigation. The used fractional operator is the Caputo derivative. In the present paper, the fractional resolvent operators have been defined and used to prove the existence of the unique solution of the fractional neutral differential equations. The fixed point theorem has been used in existence investigations. For an illustration of our results in this paper, an example has been provided as well.","PeriodicalId":505378,"journal":{"name":"An International Journal of Optimization and Control: Theories & Applications (IJOCTA)","volume":"62 12","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence and uniqueness study for partial neutral functional fractional differential equation under Caputo derivative\",\"authors\":\"N. Sene, A. Ndiaye\",\"doi\":\"10.11121/ijocta.1464\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The partial neutral functional fractional differential equation described by the fractional operator is considered in the present investigation. The used fractional operator is the Caputo derivative. In the present paper, the fractional resolvent operators have been defined and used to prove the existence of the unique solution of the fractional neutral differential equations. The fixed point theorem has been used in existence investigations. For an illustration of our results in this paper, an example has been provided as well.\",\"PeriodicalId\":505378,\"journal\":{\"name\":\"An International Journal of Optimization and Control: Theories & Applications (IJOCTA)\",\"volume\":\"62 12\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"An International Journal of Optimization and Control: Theories & Applications (IJOCTA)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.11121/ijocta.1464\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"An International Journal of Optimization and Control: Theories & Applications (IJOCTA)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11121/ijocta.1464","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Existence and uniqueness study for partial neutral functional fractional differential equation under Caputo derivative
The partial neutral functional fractional differential equation described by the fractional operator is considered in the present investigation. The used fractional operator is the Caputo derivative. In the present paper, the fractional resolvent operators have been defined and used to prove the existence of the unique solution of the fractional neutral differential equations. The fixed point theorem has been used in existence investigations. For an illustration of our results in this paper, an example has been provided as well.