Inverse problem for a time-fractional differential equation with a time- and space-integral conditions

被引：2

作者：

Kirane, Mokhtar ^{[1
,2
,3
]}

Lopushansky, Andriy ^{[4
,6
]}

Lopushanska, Halyna ^{[5
]}

机构：

[1] Khalifa Univ, Fac Arts & Sci, Dept Math, Abu Dhabi, U Arab Emirates

[2] King Abdulaziz Univ, Fac Sci, Dept Math, NAAM Res Grp, Jeddah, Saudi Arabia

[3] Univ La Rochelle, LASIE, La Rochelle, France

[4] Univ Rzeszow, Inst Informat, Rzeszow, Poland

[5] Ivan Franko Natl Univ Lviv, Dept Differential Equat, Lvov, Ukraine

[6] Univ Rzeszow, Inst Informat, 1 Pigon Str, PL-35310 Rzeszow, Poland

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2023年 / 46卷 / 15期

关键词：

fractional derivative; Green vector-function; integral condition; inverse problem; Schwartz distribution; DIFFUSION EQUATION;

D O I：

10.1002/mma.9453

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the inverse problem for a differential equation of order 2b$$ 2b $$ with the time Caputo fractional derivative and a source with values in Schwartz-type distributions. The generalized solution of the Cauchy problem for such an equation with initial values and a time-dependent reaction coefficient are unknown. We find sufficient conditions for the unique solvability of the inverse problem under a time- and space-integral overdetermination conditions.

引用

页码：16381 / 16393

页数：13

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