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On Complete Monotonicity of Solution to the Fractional Relaxation Equation with the n th Level Fractional Derivative

Author

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  • Yuri Luchko

    (Department of Mathematics, Physics, and Chemistry, Beuth Technical University of Applied Sciences Berlin, Luxemburger Str. 10, 13353 Berlin, Germany)

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. Afterwards, 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 second level derivative.

Suggested Citation

  • Yuri Luchko, 2020. "On Complete Monotonicity of Solution to the Fractional Relaxation Equation with the n th Level Fractional Derivative," Mathematics, MDPI, vol. 8(9), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1561-:d:412048
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    Cited by:

    1. António M. Lopes & J. A. Tenreiro Machado, 2022. "Nonlinear Dynamics," Mathematics, MDPI, vol. 10(15), pages 1-3, July.

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