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

Mokhtar Kirane; Andriy Lopushansky; Halyna Lopushanska

doi:10.1002/mma.9453

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

Mokhtar Kirane
, Andriy Lopushansky
, Halyna Lopushanska

Department of Mathematics
King Abdulaziz University
Université de La Rochelle
University of Rzeszow
The Ivan Franko National University of Lviv

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

7 Scopus citations

Abstract

We study the inverse problem for a differential equation of order (Figure presented.) 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.

Original language	British English
Pages (from-to)	16381-16393
Number of pages	13
Journal	Mathematical Methods in the Applied Sciences
Volume	46
Issue number	15
DOIs	https://doi.org/10.1002/mma.9453
State	Published - Oct 2023

Keywords

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

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abstract = "We study the inverse problem for a differential equation of order (Figure presented.) 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.",

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PY - 2023/10

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N2 - We study the inverse problem for a differential equation of order (Figure presented.) 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.

AB - We study the inverse problem for a differential equation of order (Figure presented.) 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.

KW - fractional derivative

KW - Green vector-function

KW - integral condition

KW - inverse problem

KW - Schwartz distribution

UR - https://www.scopus.com/pages/publications/85161432781

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DO - 10.1002/mma.9453

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JO - Mathematical Methods in the Applied Sciences

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IS - 15

ER -

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

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Keywords

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