In this article, we introduce an approach to fractional derivatives in the theory of generalized functions (Colombeau algebra G ) using the new definition of the fractional derivative called ”A New Conformable Fractional Derivative and Applications ” introduced in ” introduced in (Dα f)(t) = lim h→0f (t + he(α−1)t) − f (t) h,for all t > 0, and α ∈ (0,1). we are going to show that if f is an element of the Colombeau algebra then(Dα f )is too, as well as the integral Iα f linked to this fractional derivation and we have introduced the important remark which supports and reinforces our new definition.
In this article, we introduce an approach to fractional derivatives in the theory of generalized functions (Colombeau algebra G ) using the new definition of the fractional derivative called ”A New Conformable Fractional Derivative and Applications ” introduced in [1]” introduced in [1] (Dα f)(t) = limh→0f (t + he(α−1)t) − f (t) h for all t > 0, and α ∈ (0,1). we are going to show that if f is an element of the Colombeau algebra then(Dα f )is too, as well as the integral Iα f linked to this fractional derivation and we have introduced the important remark which supports and reinforces our new definition.