About accuracy increase of fractional order derivative and integral computations by applying the Grünwald–Letnikov formula

• Formulas for coefficients computation.
• Different schemas of function discretization.
• More points for step in summation.

The aim of the paper is to gather and to survey various formulas for fractional order derivative and integral calculations according to their Grünwald–Letnikov definition. The paper presents evaluation results for some factors, which influence its accuracy and efficiency of computations: different formulas for the coefficients calculations, different forms of the formula and different schemas for the function discretization, including more points per step of summation. It also hints how to solve some of the serious programming issues when applying the formulas. The objective is to determine a recipe for the increase the default low computational accuracy and efficiency of this popular method of fractional order derivative and integral calculations.