Special function form solutions of multi-parameter generalized Mittag-Leffler kernel based bio-heat fractional order model subject to thermal memory shocks

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F24%3A10254519" target="_blank" >RIV/61989100:27740/24:10254519 - isvavai.cz</a>

Výsledek na webu

<a href="https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0299106" target="_blank" >https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0299106</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1371/journal.pone.0299106" target="_blank" >10.1371/journal.pone.0299106</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Special function form solutions of multi-parameter generalized Mittag-Leffler kernel based bio-heat fractional order model subject to thermal memory shocks

Popis výsledku v původním jazyce

The primary objective of this research is to develop a mathematical model, analyze the dynamic occurrence of thermal shock and exploration of how thermal memory with moving line impact of heat transfer within biological tissues. An extended version of the Pennes equation as its foundational framework, a new fractional modelling approach called the Prabhakar fractional operator to investigate and a novel time-fractional interpretation of Fourier&apos;s law that incorporates its historical behaviour. This fractional operator has multi parameter generalized Mittag-Leffler kernel. The fractional formulation of heat flow, achieved through a generalized fractional operator with a non-singular type kernel, enables the representation of the finite propagation speed of heat waves. Furthermore, the dynamics of thermal source continually generates a linear thermal shock at predefined locations within the tissue. Introduced the appropriate set of variables to transform the governing equations into dimensionless form. Laplace transform (LT) is operated on the fractional system of equations and results are presented in series form and also expressed the solution in the form of special functions. The article derives analytical solutions for the heat transfer phenomena of both the generalized model, in the Laplace domain, and the ordinary model in the real domain, employing Laplace inverse transformation. The pertinent parameter&apos;s influence, such as α, β, γ, a0, b0, to gain insights into the impact of the thermal memory parameter on heat transfer, is brought under consideration to reveal the interesting results with graphical representations of the findings.

Název v anglickém jazyce

Special function form solutions of multi-parameter generalized Mittag-Leffler kernel based bio-heat fractional order model subject to thermal memory shocks

Popis výsledku anglicky

The primary objective of this research is to develop a mathematical model, analyze the dynamic occurrence of thermal shock and exploration of how thermal memory with moving line impact of heat transfer within biological tissues. An extended version of the Pennes equation as its foundational framework, a new fractional modelling approach called the Prabhakar fractional operator to investigate and a novel time-fractional interpretation of Fourier&apos;s law that incorporates its historical behaviour. This fractional operator has multi parameter generalized Mittag-Leffler kernel. The fractional formulation of heat flow, achieved through a generalized fractional operator with a non-singular type kernel, enables the representation of the finite propagation speed of heat waves. Furthermore, the dynamics of thermal source continually generates a linear thermal shock at predefined locations within the tissue. Introduced the appropriate set of variables to transform the governing equations into dimensionless form. Laplace transform (LT) is operated on the fractional system of equations and results are presented in series form and also expressed the solution in the form of special functions. The article derives analytical solutions for the heat transfer phenomena of both the generalized model, in the Laplace domain, and the ordinary model in the real domain, employing Laplace inverse transformation. The pertinent parameter&apos;s influence, such as α, β, γ, a0, b0, to gain insights into the impact of the thermal memory parameter on heat transfer, is brought under consideration to reveal the interesting results with graphical representations of the findings.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10300 - Physical sciences

Projekt

—

Návaznosti

—

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

PLoS One

ISSN

1932-6203

e-ISSN

1932-6203

Svazek periodika

19

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

15

Strana od-do

—

Kód UT WoS článku

001181701200028

EID výsledku v databázi Scopus

2-s2.0-85187506905