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General fractional calculus operators containing the generalized Mittag-Leffler functions applied to anomalous relaxation

Yang Xiaojun (China University of Mining and Technology, State Key Laboratory for Geomechanics and Deep Underground Engineering, Xuzhou, P.R. China + China University of Mining and Technology, School of Mechanics and Civil Engineering, Xuzhou, P.R. China)

In this paper, we address a family of the general fractional calculus operators of Wiman and Prabhakar types for the first time. The general Mittag-Leffler function to structure the kernel functions of the fractional order derivative operators and their Laplace integral transforms are considered in detail. The formulations are as the mathematical tools proposed to investigate the anomalous relaxation.

Keywords: General fractional calculus operators, Mittag-Leffler function, general Mittag-Leffler function, anomalous relaxation