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In this article, a general fractional-order derivative of the Riemann-Liouville type with the non-singular kernel involving the Rabotnov fractional-exponential function is addressed for the first time. A new general fractional-order derivative model for the anomalous diffusion is discussed in detail. The general fractional-order derivative operator formula is as a novel and mathematical approch proposed to give the generalized presentation of the physical models in complex phenomena with power law.
PAPER REVISED: 2018-10-11
PAPER ACCEPTED: 2018-12-22
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