Abstract
Abstract
The paper investigates a second-order differential equation with a fractional derivative in the lower term, in which the order of the fractional derivative is in the range from zero to two and is not known in advance. This model is used to describe oscillatory processes in a viscous medium. A fundamentally new method has been developed for the approximate solution of the first boundary-value problem for the equation of string vibration taking into account friction in a medium with fractal geometry. Considering that polymer concrete is a set of granules of a mineral filler located in a viscous medium, the equation of motion of these granules is derived and investigated. A technique is proposed for studying the motion of granules in a medium with fractal geometry.
Subject
General Physics and Astronomy
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