Fractional Derivative as Fractional Power of Derivative
arXiv:0711.2567 · doi:10.1142/S0129167X07004102
Abstract
Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of self-adjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.
20 pages, LaTeX
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