On the generalized fractional derivatives and their Caputo modification

In this manuscript, we define the generalized fractional derivative on ACγ [a,b], the space of functions defined on [a,b] such that γn−1f ∈ AC[a,b], where γ = x1−ρ d dx . We present some of the properties of generalized fractional derivatives of these functions and then we define their Caputo version. c ©2017 All rights reserved.

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