Recovering the space source term for the fractional-diffusion equation with Caputo-Fabrizio derivative

被引：6

作者：

Le Nhat Huynh ^{[1
]}

Nguyen Hoang Luc ^{[2
]}

Baleanu, Dumitru ^{[3
,4
,5
]}

Le Dinh Long ^{[2
]}

机构：

[1] Ton Duc Thang Univ, Fac Math & Stat, Appl Anal Res Grp, Ho Chi Minh City, Vietnam

[2] Thu Dau Mot Univ, Div Appl Math, Thu Dau Mot, Binh Duong Prov, Vietnam

[3] Cankaya Univ, Dept Math, Ankara, Turkey

[4] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung, Taiwan

[5] Inst Space Sci, Magurele, Romania

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2021年 / 2021卷 / 01期

关键词：

Source function; Fractional diffusion equation; Caputo-Fabrizio fractional derivative; Regularization method; 26A33; 35B65; 35R11;

D O I：

10.1186/s13660-021-02557-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article is devoted to the study of the source function for the Caputo-Fabrizio time fractional diffusion equation. This new definition of the fractional derivative has no singularity. In other words, the new derivative has a smooth kernel. Here, we investigate the existence of the source term. Through an example, we show that this problem is ill-posed (in the sense of Hadamard), and the fractional Landweber method and the modified quasi-boundary value method are used to deal with this inverse problem and the regularized solution is also obtained. The convergence estimates are addressed for the regularized solution to the exact solution by using an a priori regularization parameter choice rule and an a posteriori parameter choice rule. In addition, we give a numerical example to illustrate the proposed method.

引用

页数：20