The Fourier law correctly describes heat transport in most practical macroscopic problems.
However, for heat transfer in rapid processes, heat transport on micro-and nanoscales, and …

The Jeffreys-type heat conduction equation with flux precedence describes the temperature
of diffusive hot electrons during the electron–phonon interaction process in metals. In this …

The nonlinear fourth-order reaction–subdiffusion equation whose solutions display a typical
initial weak singularity is considered. A new analytical technique is introduced to analyze …

Abstract Recent studies (see Rukolaine 2014, 2017) have deduced solutions of the
parabolic and hyperbolic dual-phase-lag (DPL) models in the three-dimensional space …

Nanoscale heat transfer cannot be described by the classical Fourier law due to the very
small dimension, and therefore, analyzing heat transfer in nanoscale is of crucial importance …

Recent studies highlight that diffusion processes in highly heterogeneous, fractal-like media
can exhibit anomalous transport phenomena, which motivates us to consider the use of …

In this paper, we develop a finite difference method for solving the wave equation with
fractional damping in 1D and 2D cases, where the fractional damping is given based on the …

In this study, a time fractional dual-phase-lag model with temperature jump boundary
condition as a choice for the Fourier's law replacement in thermal modeling of transistors, is …

In this paper, based on the nonuniform time meshes, we proposed an efficient difference
scheme for solving the time-fractional bi-flux diffusion equation. By the energy method, we …

This paper presents a new semi-explicit algorithm for parameters estimation in a time-
fractional generalization of a dual-phase-lag heat conduction model with Caputo fractional …