Stability of a fractional heat equation with memory

S. Kerbal; N. Tatar

doi:10.15330/cmp.16.1.328-345

Stability of a fractional heat equation with memory

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

Abstract

Of concern is a fractional differential problem of order between zero and one. The model generalizes an existing well-known problem in heat conduction theory with memory. First, we justify the replacement of the first order derivative by a fractional one. Then, we establish a Mittag-Leffler stability result for a class of heat flux relaxation functions. We will combine the energy method with some properties from fractional calculus.

Original language	English
Pages (from-to)	328-345
Number of pages	18
Journal	Carpathian Mathematical Publications
Volume	16
Issue number	1
DOIs	https://doi.org/10.15330/cmp.16.1.328-345
State	Published - 30 Jun 2024

Bibliographical note

Publisher Copyright:
© Kerbal S., Tatar N., 2024.

Keywords

Caputo fractional derivative
heat-conduction
memory term
Mittag-Leffler stability
multiplier technique

ASJC Scopus subject areas

General Mathematics

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10.15330/cmp.16.1.328-345

Cite this

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abstract = "Of concern is a fractional differential problem of order between zero and one. The model generalizes an existing well-known problem in heat conduction theory with memory. First, we justify the replacement of the first order derivative by a fractional one. Then, we establish a Mittag-Leffler stability result for a class of heat flux relaxation functions. We will combine the energy method with some properties from fractional calculus.",

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Y1 - 2024/6/30

N2 - Of concern is a fractional differential problem of order between zero and one. The model generalizes an existing well-known problem in heat conduction theory with memory. First, we justify the replacement of the first order derivative by a fractional one. Then, we establish a Mittag-Leffler stability result for a class of heat flux relaxation functions. We will combine the energy method with some properties from fractional calculus.

AB - Of concern is a fractional differential problem of order between zero and one. The model generalizes an existing well-known problem in heat conduction theory with memory. First, we justify the replacement of the first order derivative by a fractional one. Then, we establish a Mittag-Leffler stability result for a class of heat flux relaxation functions. We will combine the energy method with some properties from fractional calculus.

KW - Caputo fractional derivative

KW - heat-conduction

KW - memory term

KW - Mittag-Leffler stability

KW - multiplier technique

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Stability of a fractional heat equation with memory

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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