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\begin{document}

\title{On the distributional fractional derivative: from unidimensional to
multidimensional}



\author[1]{ABDERACHID SAADI}%
\affil[1]{Universite Mohamed Boudiaf M'sila}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\begin{abstract}
In this paper, we use the generalized notions of Riemann-Liouville
(fractional calculus with respect to a regular function \selectlanguage{greek}\emph{σ}\selectlanguage{english}) to
extend the definitions of fractional integration and derivative from the
functional sense to the distributional sense. First, we give some
properties of fractional integral and derivative for the functions
infinitely differentiable with compact support. Then, we define the weak
derivative, as well as the integral and derivative of a distribution
with compact support, the integral and derivative of a distribution
using the convolution product. Then, we generalize those concepts from
the unidimensional to the multidimensional case. Finally, we propose the
definitions of some usual differential operators.%
\end{abstract}%



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