The Regional Enlarged Observability for Hilfer Fractional Differential Equations

被引：1
|
作者：
Elbukhari, Abu Bakr [1 ,2 ]
Fan, Zhenbin [1 ]
Li, Gang [1 ]
机构：
[1] Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Peoples R China
[2] Univ Khartoum, Fac Educ, Dept Math, Omdurman 406, Sudan
来源：
AXIOMS | 2023年 / 12卷 / 07期
基金：
中国国家自然科学基金;
关键词：
Hilfer fractional derivatives; fractional diffusion systems; regional enlarged observability; Hilbert uniqueness method; SYSTEMS;
D O I：
10.3390/axioms12070648
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the concept of regional enlarged observability (ReEnOb) for fractional differential equations (FDEs) with the Hilfer derivative. To proceed this, we develop an approach based on the Hilbert uniqueness method (HUM). We mainly reconstruct the initial state ?(1)(0) on an internal subregion ? from the whole domain O with knowledge of the initial information of the system and some given measurements. This approach shows that it is possible to obtain the desired state between two profiles in some selective internal subregions. Our findings develop and generalize some known results. Finally, we give two examples to support our theoretical results.
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页数：19
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