Inverse problem for a time‐fractional differential equation with a time‐ and space‐integral conditions-Reference-Cited by-同舟云学术

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

Published:2023-06-06 Issue:15 Volume:46 Page:16381-16393
ISSN:0170-4214
Container-title:Mathematical Methods in the Applied Sciences
language:en
Short-container-title:Math Methods in App Sciences

Author:

Kirane Mokhtar¹²³,Lopushansky Andriy⁴^ORCID,Lopushanska Halyna⁵

Affiliation:

1. Department of Mathematics, Faculty of Arts and Science Khalifa University Abu Dhabi United Arab Emirates

2. NAAM Research Group, Department of Mathematics, Faculty of Science King Abdulaziz University Jeddah Saudi Arabia

3. LASIE University of La Rochelle La Rochelle France

4. Institute of Informatics University of Rzeszów Rzeszów Poland

5. Department of Differential Equations Ivan Franko National University of Lviv Lviv Ukraine

Abstract

We study the inverse problem for a differential equation of order 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.

Publisher

Wiley

Subject

General Engineering,General Mathematics

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/mma.9453

Reference24 articles.

1. Global existence and asymptotic behavior for a time fractional reaction–diffusion system

2. Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type

3. The Cauchy problem for evolutionary equation of fractional order;Kochubei A. N.;Differ. Equ.,1989

4. The fundamental solutions for the fractional diffusion-wave equation