Approximation and application of the Riesz-Caputo fractional derivative of variable order with fixed memory

In this paper, the Riesz-Caputo fractional derivative of variable order with fixed memory is considered. The studied non-integer differential operator is approximated by means of modified basic rules of numerical integration. The three proposed methods are based on polynomial interpolation: piecewise constant, piecewise linear, and piecewise quadratic interpolation. The errors generated by the described methods and the experimental rate of convergence are reported. Finally, an application of the Riesz-Caputo fractional derivative of space-dependent order in continuum mechanics is depicted.