期刊
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
卷 22, 期 1-3, 页码 92-94出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2014.07.022
关键词
Counterexample; Fractional calculus; Modified Riemann-Liouville's derivative
类别
资金
- Natural Science Foundation of Heilongjiang Province of China [A201308]
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.
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