Role of the Virtual Boundary Layer in One-Dimensional Fractional Elasticity Problems

Abstract

In this paper the influence of the virtual boundary layer on a fractional continuum is under consideration. The virtual boundary layer appears as a consequence of the definition of a both-sided fractional derivative, which is the basic operator in the description. The paper studies the one-dimensional elasticity problem under different boundary conditions, together with a range of length scales applied and different orders of fractional continua.