A New Conformable Fractional Derivative In Generalized Functions

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) = 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.

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The authors declare no conflict of interest.

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The datasets used in this study are openly available at [repository link] and the source code is available on GitHub at [GitHub link].

This work did not receive any external funding.