Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 18, Issue 11, Pages 2945-2948Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2013.04.001
Keywords
Fractional derivative; Leibniz rule
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We demonstrate that a violation of the Leibniz rule is a characteristic property of derivatives of non-integer orders. We prove that all fractional derivatives D-alpha, which satisfy the Leibniz rule D(alpha()fg) = (D(alpha)f) g + f(D(alpha)g), should have the integer order alpha = 1, i.e. fractional derivatives of non-integer orders cannot satisfy the Leibniz rule. (C) 2013 Elsevier B. V. All rights reserved.
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