The General Fractional Integrals and Derivatives on a Finite Interval

The general fractional integrals and derivatives considered so far in the Fractional Calculus literature have been defined for functions on real positive semi-axis. main contribution of this paper is introducing a finite interval. As case Riemann–Liouville interval, we define both left- right-sided operators investigate their interconnections. results presented are 1st 2nd fundamental theorems formulated interval as well formulas integration by parts that involve derivatives.