On a Leibnitz-type fractional derivative
  A type of fractional derivative, referred to as \alpha-derivative, is studied. The \alpha-derivative of fractional type obeys Leibnitz rule. Based on the definition of \alpha-derivative the operations of analysis and differential geometry are studied It was recently proved, that this variant of introduction of the derivative leads to a new scaling of the common Leibniz derivative, but not to a alternative type of derivation. In other words, all derivatives, that satisfy the Leibniz rule, are algebraically equivalent. 
V. V. Kobelev
math-ph math.MP nlin.CD nlin.SI