The general form of a differential equation that deduces a size dependence of the surface tension is derived. The well-known Gibbs-Tolman-Koenig-Buff equation for the spherical surface is a particular case of the newly derived one. Analytical solutions to this equation for the spherical, cylindrical, parabolic, and conical surfaces are found.

A model of forced oscillations of an oscillator based on the fractional integro-differential formalism has been considered. It is shown that this model is in good agreement with the classical model...

An analog of the Lagrange equation with a fractional derivative with respect to time is derived using the principle of least action. Based on this approach, a new equation of motion is obtained and th

We consider a diffusion–wave equation with fractional derivative with respect to the time variable, defined on infinite interval, and with the starting point at minus infinity. For this equation, we solve an asympotic boundary value problem without initial conditions, construct a representation of its solution, find out sufficient conditions providing solvability and solution uniqueness, and give some applications in fractional electrodynamics.

Crack formation in electrochemical porous silicon has been experimentally and theoretically studied. It is established that the kinetics of porous silicon cracking can be described by the S-shaped Weibull distribution. This feature appears to be of general character; it may be observed during crack formation in other porous solid materials.