In this present study we review the fractional operations for some elementary and special functions and we generalize the idea of fractional operations to linear functional in the sense of generalized functions spaces. We provide several examples in order to illustrate the geometric interpretations of Dirac delta type functions. Further gave several counterexamples that the fractional derivatives of distributions need not necessarily to be elementary functions rather appear as the hypergeometric functions. 
Keywords: Fractional derivatives; linear functional; Dirac delta function; generalized functions; hypergeometric functions

Adem KILICMAN is a full Professor in the Department of Mathematics at Universiti Putra Malaysia. He received his Bachelor and Master degrees from Hacettepe University in 1989 and 1991 respectively, Turkey. He obtained his PhD from University of Leicester in 1995, United Kingdom. He has been actively involved several academic activities in the Faculty of Science and Institute of Mathematical Research (INSPEM). Adem Kilicman is also Editorial Member of some international journals. He has been invited in many International Conferences as plenary speakers as well as invited talks. His research areas include Differential Equations, Functional Analysis and Topology. He has supervised many postgraduate students and has successfully published almost 400 papers in national and international highly repute journals.