On the generalized fractional derivatives and their Caputo modification

In this manuscript, we define the generalized fractional derivative on \ (ACⁿ_ a, b\), the space of functions defined on a, b such that \ (^n-1f ACa, b\), where \ (=x^1-pddx\). We present some of the properties of generalized fractional derivatives of these functions and then we define their Caputo version.