On selected aspects of space-fractional continuum mechanics model approximation

The main goal of this paper is to study selected aspects of the space-Fractional Continuum Mechanical model (s-FCM) approximation. The considerations include the in-depth analysis of three generalized finite difference schemes, which are based on: (i) The rectangle rule, (ii) the trapezoidal rule, and (iii) Simpson’s (parabolas) rule, respectively. The analysis includes the dynamic (eigenvalues) response of the 1D s-FCM body.