A family of the Cauchy type mean-value theorems

AbstractThe Cauchy type mean-value theorems for the Riemann–Liouville fractional derivative are deduced here from known mean-value theorems of the Lagrange type. A general method for deducing these Cauchy type formulas is extracted. Two Cauchy type formulas are then deduced without a priori knowledge about the Lagrange type mean-value theorems