Temperature profile and thermal piston component of photoacoustic response calculated by the fractional dual-phase-lag heat conduction theory

Mathematical Modeling of Anomalous Diffusive Behavior in Transdermal Drug-Delivery Including Time-Delayed Flux Concept

“…Some of examples of anomalous diffusion are charge carrier motion in amorphous semiconductors [10,11], molecular motor-driven motion in biological cells [12,13], motion of particles in crowded environments such as biological membranes [14][15][16], chemical migration in porous media [17,18], etc. It is interesting to note that similar problems occur in the heat transport problems where classic diffusion theory of heat conduction cannot explain experimentally observed anomalous effects [19][20][21].…”

“…More recently, by the end of the twentieth century, it turned out that some physical phenomena are modeled more accurately when fractional calculus is used [81]. Typical examples of the use of fractal derivatives can be found in physics and mathematics [19][20][21][81][82][83][84][85], in bioengineering [86], in geophysics [87], in polymers physics [88], etc. Tateishi et al [80] recently described how the diffusion in complex systems can be accurately addressed with fractional time-derivative operator.…”

Influence of Local Thermodynamic Non-Equilibrium to Photothermally Induced Acoustic Response of Complex Systems

“…Photoacoustic (PA) and other photothermal (PT) techniques are non-destructive experimental methods based on recording of detectable phenomena produced by optically induced heat transfer across the illuminated sample [1][2][3][4][5][6][7][8]. These techniques have been developed for the last half century and are increasingly being applied in measuring the thermal properties of various samples [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”