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Exact results for a fractional derivative of elementary functions. (arXiv:1711.07126v3 [math-ph] UPDATED)
来源于:arXiv
We present exact analytical results for the Caputo fractional derivative of a
wide class of elementary functions, including trigonometric and inverse
trigonometric, hyperbolic and inverse hyperbolic, Gaussian, quartic Gaussian,
and Lorentzian functions. These results are especially important for
multi-scale physical systems, such as porous materials, disordered media, and
turbulent fluids, in which transport is described by fractional partial
differential equations. The exact results for the Caputo fractional derivative
are obtained from a single generalized Euler's integral transform of the
generalized hyper-geometric function with a power-law argument. We present a
proof of the generalized Euler's integral transform and directly apply it to
the exact evaluation of the Caputo fractional derivative of a broad spectrum of
functions, provided that these functions can be expressed in terms of a
generalized hyper-geometric function with a power-law argument. We determine
that the Caputo fr 查看全文>>