Multi-fractional-differential operators for a thermo-elastic magnetic response in an unbounded solid with a spherical hole via the DPL model

Moaaz, Osama; Abouelregal, Ahmed E.

doi:10.3934/math.2023282

Cited by 2 publications

(2 citation statements)

References 62 publications

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“…Taking into account the enormous mentioned properties, many researchers paid attention to analyse the fractional behaviour of different fluid models directly or indirectly in case of derivatives when it is considered as non-integer order from. Instantaneous heat conduction and local thermal equilibrium are presupposed in these models [17][18][19][20]. Bagley and Torvik [21] noted the fractional calculus application on the viscoelastic fluids.…”

Section: Introductionmentioning

confidence: 99%

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

Riaz,

Rehman,

Martinovic

et al. 2024

PLoS ONE

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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’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’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.

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Section: Introductionmentioning

confidence: 99%

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

Riaz,

Rehman,

Martinovic

et al. 2024

PLoS ONE

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“…The Pennes bioheat equation and other conventional partial differential equations have been used to model heat transfer in biological tissues. Instantaneous heat conduction and local thermal equilibrium are presupposed in these models [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Bioheat Transfer with Thermal Memory and Moving Thermal Shocks

Shah,

Almutairi,

Vieru

et al. 2023

Fractal Fract

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This article investigates the effects of thermal memory and the moving line thermal shock on heat transfer in biological tissues by employing a generalized form of the Pennes equation. The mathematical model is built upon a novel time-fractional generalized Fourier’s law, wherein the thermal flux is influenced not only by the temperature gradient but also by its historical behavior. Fractionalization of the heat flow via a fractional integral operator leads to modeling of the finite speed of the heat wave. Moreover, the thermal source generates a linear thermal shock at every instant in a specified position of the tissue. The analytical solution in the Laplace domain for the temperature of the generalized model, respectively the analytical solution in the real domain for the ordinary model, are determined using the Laplace transform. The influence of the thermal memory parameter on the heat transfer is analyzed through numerical simulations and graphic representations.

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Multi-fractional-differential operators for a thermo-elastic magnetic response in an unbounded solid with a spherical hole via the DPL model

Cited by 2 publications

References 62 publications

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

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

Bioheat Transfer with Thermal Memory and Moving Thermal Shocks

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