On selected aspects of space-Fractional Continuum Mechanics model approximation

Abstract 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. In the numerical study special emphasis is placed on the relationship between fundamental s-FCM model (material) parameters (the order of continua and the length scale) and the quality of approximation.