On initial value problem for elliptic equation on the plane under Caputo derivative

被引:1
作者
Binh, Tran Thanh [2 ]
Thang, Bui Dinh [2 ]
Phuong, Nguyen Duc [1 ]
机构
[1] Ind Univ Ho Chi Minh, Fac Fundamental Sci, Ho Chi Minh City, Vietnam
[2] Sai Gon Univ, Fac Math & Applicat, Ho Chi Minh City, Vietnam
关键词
fractional elliptic equation; Caputo derivative; Mittag-Leffler functions; DIFFERENTIAL-EQUATION; CAUCHY-PROBLEM; CONTINUITY; REGULARITY; OPERATORS;
D O I
10.1515/dema-2022-0257
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this article, we are interested to study the elliptic equation under the Caputo derivative. We obtain several regularity results for the mild solution based on various assumptions of the input data. In addition, we derive the lower bound of the mild solution in the appropriate space. The main tool of the analysis estimation for the mild solution is based on the bound of the Mittag-Leffler functions, combined with analysis in Hilbert scales space. Moreover, we provide a regularized solution for our problem using the Fourier truncation method. We also obtain the error estimate between the regularized solution and the mild solution. Our current article seems to be the first study to deal with elliptic equations with Caputo derivatives on the unbounded domain.
引用
收藏
页数:15
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