Fractional telegrapher’s equation as a consequence of Cattaneo’s heat conduction law generalization

Zorica, Dušan; Cveticanin, M Stevan

doi:10.2298/tam171211003z

Cited by 4 publications

(1 citation statement)

References 26 publications

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“…Various time-fractional generalizations of the integer-order non-Fourier heat conduction models are studied. Fractional telegrapher's equation are considered, e.g., in [16][17][18], while the works [19,20] are devoted to fractional Cattaneo-type equations of distributed order. In [21] a number of time-fractional Cattaneo models are shown to produce the crossover of the mean squared displacement from superdiffusion to subdiffusion.…”

Section: Introduction and Model Formulationmentioning

confidence: 99%

Transition from Diffusion to Wave Propagation in Fractional Jeffreys-Type Heat Conduction Equation

Bazhlekova

Bazhlekov

2020

Fractal Fract

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The heat conduction equation with a fractional Jeffreys-type constitutive law is studied. Depending on the value of a characteristic parameter, two fundamentally different types of behavior are established: diffusion regime and propagation regime. In the first case, the considered equation is a generalized diffusion equation, while in the second it is a generalized wave equation. The corresponding memory kernels are expressed in both cases in terms of Mittag–Leffler functions. Explicit representations for the one-dimensional fundamental solution and the mean squared displacement are provided and analyzed analytically and numerically. The one-dimensional fundamental solution is shown to be a spatial probability density function evolving in time, which is unimodal in the diffusion regime and bimodal in the propagation regime. The multi-dimensional fundamental solutions are probability densities only in the diffusion case, while in the propagation case they can have negative values. In addition, two different types of subordination principles are formulated for the two regimes. The Bernstein functions technique is extensively employed in the theoretical proofs.

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Section: Introduction and Model Formulationmentioning

confidence: 99%

Transition from Diffusion to Wave Propagation in Fractional Jeffreys-Type Heat Conduction Equation

Bazhlekova

Bazhlekov

2020

Fractal Fract

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Transmission line modeling by fractional and topological generalization of the telegrapher's equation

Zorica

Cvetićanin

2022

Fractional-Order Modeling of Dynamic Systems With Applications in Optimization, Signal Processing and Control

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Subordination in a Class of Generalized Time-Fractional Diffusion-Wave Equations

Bazhlekova

2018

FCAA

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Motivated by recently proposed generalizations of the diffusion-wave equation with the Caputo time fractional derivative of order α ∈ (1, 2), in the present survey paper a class of generalized time-fractional diffusion-wave equations is introduced. Its definition is based on the subordination principle for Volterra integral equations and involves the notion of complete Bernstein function. Various members of this class are surveyed, including the distributed-order time-fractional diffusion-wave equation and equations governing wave propagation in viscoelastic media with completely monotone relaxation moduli.

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Fractional telegrapher’s equation as a consequence of Cattaneo’s heat conduction law generalization

Cited by 4 publications

References 26 publications

Transition from Diffusion to Wave Propagation in Fractional Jeffreys-Type Heat Conduction Equation

Transition from Diffusion to Wave Propagation in Fractional Jeffreys-Type Heat Conduction Equation

Transmission line modeling by fractional and topological generalization of the telegrapher's equation

Subordination in a Class of Generalized Time-Fractional Diffusion-Wave Equations

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