We consider the time-fractional Cattaneo equation involving the tempered Caputo space-fractional derivative. There is an increasing interest in the recent literature for the applications of the fractional-type Cattaneo ...

The Stefan problem, involving the tracking of an evolving phase-change front, is the prototypical example of a moving boundary problem. In basic one- dimensional problems it is well known that the front advances as the ...

The dynamics of transients of fluid-rock temperature, pore pressure, pollutants in porous rocks are of vivid interest for fundamental problems in hydrological, volcanic, hydrocarbon systems, deep oil drilling. This can ...

In the Fourier heat conduction equation, when the flux definition is expressed as the product of a constant diffusivity and the temperature gradient, the characteristic length scale evolves as the square root of time. ...

From the point of view of the general theory of the hyper-Bessel operators, we consider a particular operator that is suitable to generalize the standard process of relaxation by taking into account both memory effects of ...