No violation of the Leibniz rule. No fractional derivative

被引：234

作者：

Tarasov, Vasily E. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Skobeltsyn Inst Nucl Phys, Moscow 119991, Russia

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2013年 / 18卷 / 11期

关键词：

Fractional derivative; Leibniz rule;

D O I：

10.1016/j.cnsns.2013.04.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：2945 / 2948

页数：4

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