Determination of two unknown functions of different variables in a time-fractional differential equation

Mokhtar Kirane; Andriy Lopushansky; Halyna Lopushanska

doi:10.1002/mma.10539

Determination of two unknown functions of different variables in a time-fractional differential equation

Mokhtar Kirane
, Andriy Lopushansky
, Halyna Lopushanska

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We study the inverse problem for a differential equation of (Formula presented.) -order with the Caputo fractional derivative over time and Schwartz-type distribution in its right-hand side. The generalized solution of the Cauchy problem for such an equation, space-dependent part of a source, and a time-dependent reaction coefficient in the equation are unknown. We find sufficient conditions for unique local in time solvability of the inverse problem under time- and space-integral overdetermination conditions.

Original language	British English
Pages (from-to)	4185-4194
Number of pages	10
Journal	Mathematical Methods in the Applied Sciences
Volume	48
Issue number	4
DOIs	https://doi.org/10.1002/mma.10539
State	Published - 15 Mar 2025

Keywords

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

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10.1002/mma.10539

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abstract = "We study the inverse problem for a differential equation of (Formula presented.) -order with the Caputo fractional derivative over time and Schwartz-type distribution in its right-hand side. The generalized solution of the Cauchy problem for such an equation, space-dependent part of a source, and a time-dependent reaction coefficient in the equation are unknown. We find sufficient conditions for unique local in time solvability of the inverse problem under time- and space-integral overdetermination conditions.",

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author = "Mokhtar Kirane and Andriy Lopushansky and Halyna Lopushanska",

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T1 - Determination of two unknown functions of different variables in a time-fractional differential equation

AU - Kirane, Mokhtar

AU - Lopushansky, Andriy

AU - Lopushanska, Halyna

PY - 2025/3/15

Y1 - 2025/3/15

N2 - We study the inverse problem for a differential equation of (Formula presented.) -order with the Caputo fractional derivative over time and Schwartz-type distribution in its right-hand side. The generalized solution of the Cauchy problem for such an equation, space-dependent part of a source, and a time-dependent reaction coefficient in the equation are unknown. We find sufficient conditions for unique local in time solvability of the inverse problem under time- and space-integral overdetermination conditions.

AB - We study the inverse problem for a differential equation of (Formula presented.) -order with the Caputo fractional derivative over time and Schwartz-type distribution in its right-hand side. The generalized solution of the Cauchy problem for such an equation, space-dependent part of a source, and a time-dependent reaction coefficient in the equation are unknown. We find sufficient conditions for unique local in time solvability of the inverse problem under time- and space-integral overdetermination conditions.

KW - fractional derivative

KW - Green vector-function

KW - integral condition

KW - inverse problem

KW - Schwartz distribution

UR - https://www.scopus.com/pages/publications/85205954195

U2 - 10.1002/mma.10539

DO - 10.1002/mma.10539

M3 - Article

AN - SCOPUS:85205954195

SN - 0170-4214

VL - 48

SP - 4185

EP - 4194

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 4

ER -

Determination of two unknown functions of different variables in a time-fractional differential equation

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