A generalization of the Leibniz rule for derivatives
نویسنده
چکیده
There are m ways of allocating n labeled balls to m empty boxes. Each possibility will be referred to as an allocation. The occupancy vector (α1, . . . , αm) denotes an allocation having αi balls (αi ≥ 0) in the i-th box. The number of ways of allocating α1 labeled balls in the 1st box, α2 labeled balls in the 2nd box, . . . , αm labeled balls in the m-th box is given by the multinomial coefficient
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On The Leibniz Rule And Fractional Derivative For Differentiable And Non-Differentiable Functions
In the recent paper Communications in Nonlinear Science and Numerical Simulation. Vol.18. No.11. (2013) 2945-2948, it was demonstrated that a violation of the Leibniz rule is a characteristic property of derivatives of non-integer orders. It was proved that all fractional derivatives Dα, which satisfy the Leibniz rule Dα(fg) = (Dαf) g+ f (Dαg), should have the integer order α = 1, i.e. fraction...
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