Geodesic
Fractional Derivatives in Spaces of Generalized Functions
Fractional calculus and applied analysis, Tome 14 (2011) no. 1, pp. 125-137.

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We generalize the two forms of the fractional derivatives (in Riemann-Liouville and Caputo sense) to spaces of generalized functions using appropriate techniques such as the multiplication of absolutely continuous function by the Heaviside function, and the analytical continuation. As an application, we give the two forms of the fractional derivatives of discontinuous functions in spaces of distributions.
Keywords: Fractional Derivatives, Spaces of Generalized Functions, Fractional Derivatives of Discontinuous Function, Analytical Continuation 
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     author = {Stojanovi\'c, Mirjana},
     title = {Fractional {Derivatives} in {Spaces} of {Generalized} {Functions}},
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Stojanović, Mirjana. Fractional Derivatives in Spaces of Generalized Functions. Fractional calculus and applied analysis, Tome 14 (2011) no. 1, pp. 125-137. http://geodesic.mathdoc.fr/item/FCAA_2011_14_1_a7/