We compare three different types of
-difference fractional operators: Grünwald-Letnikov, Caputo, Riemann-Liouville types of operators. There is introduced the formula for fundamental matrix of solutions for linear systems of
-difference fractional equations with Grünwald-Letnikov type operator while the one with Caputo type or Riemann-Liouville type is well known. We present new formulas for linear control systems with the mentioned operators.