On complete monotonicity of solution to the fractional relaxation equation with the $n$th level fractional derivative

Abstract

In this paper, we first deduce the explicit formulas for the projector of the $n$th level fractional derivative and for its Laplace transform. Then the fractional relaxation equation with the $n$th level fractional derivative is discussed. It turns out that under some conditions, the solutions to the initial-value problems for this equation are completely monotone functions that can be represented in form of the linear combinations of the Mittag-Leffler functions with some power law weights. Special attention is given to the case of the relaxation equation with the 2nd level derivative.

arXiv comment15 pages, 1 figure

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• Trends, Directions for Further Research, and Some Open Problems of Fractional Calculus
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