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Research Papers

Leibniz Rule and Fractional Derivatives of Power Functions

[+] Author and Article Information
Vasily E. Tarasov

Skobeltsyn Institute of Nuclear Physics,
Lomonosov Moscow State University,
Moscow 119991, Russia
e-mail: tarasov@theory.sinp.msu.ru

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 14, 2015; final manuscript received August 17, 2015; published online October 23, 2015. Assoc. Editor: Gabor Stepan.

J. Comput. Nonlinear Dynam 11(3), 031014 (Oct 23, 2015) (4 pages) Paper No: CND-15-1215; doi: 10.1115/1.4031364 History: Received July 14, 2015; Revised August 17, 2015

In this paper, we prove that unviolated simple Leibniz rule and equation for fractional-order derivative of power function cannot hold together for derivatives of orders α1. To prove this statement, we use an algebraic approach, where special form of fractional-order derivatives is not applied.

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Grahic Jump Location
Fig. 1

Plot of the function Z(x) (Eq. (24)) for the range x=α∈[0;1.5]

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