Counterexamples on Jumarie's two basic fractional calculus formulae

Jumarie proposed a modified Riemann-Liouville derivative definition and gave two basic fractional calculus formulae (u(t)v(t))((alpha)) = u((alpha))(t)v(t) + u(t)v((alpha))(t) and (f(u(t)))((alpha)) = f'(u)u((alpha))(t) give two counterexamples to show that Jumarie's two formulae are not true. Respectively, all results obtained in references by using Jumarie's these two formulae are incorrect. In the end, we give the corresponding formulae. (C) 2014 Elsevier B.V. All rights reserved.