On Complete Monotonicity of Solution to the Fractional Relaxation Equation with the nth Level Fractional Derivative
Author:
Open Access
- 11 September 2020
- journal article
- research article
- Published by MDPI AG in Mathematics
- Vol. 8 (9) , 1561
Abstract
In this paper, we first deduce the explicit formulas for the projector of the nth level fractional derivative and for its Laplace transform. Afterwards, the fractional relaxation equation with the nth 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.Keywords
All Related Versions
This publication has 17 references indexed in Scilit:
- A Comment on a Controversial Issue: A Generalized Fractional Derivative Cannot Have a Regular KernelFractional Calculus and Applied Analysis, 2020
- Caputo–Fabrizio operator in terms of integer derivatives: memory or distributed lag?Computational and Applied Mathematics, 2019
- Desiderata for Fractional Derivatives and IntegralsMathematics, 2019
- Fractional-order derivatives defined by continuous kernels are too restrictiveApplied Mathematics Letters, 2018
- A critical analysis of the Caputo–Fabrizio operatorCommunications in Nonlinear Science and Numerical Simulation, 2018
- A comment on some new definitions of fractional derivativeNonlinear Dynamics, 2018
- What is a fractional derivative?Journal of Computational Physics, 2015
- No violation of the Leibniz rule. No fractional derivativeCommunications in Nonlinear Science and Numerical Simulation, 2013
- Bernstein Functions2009
- A note on the fractional calculusProceedings of the Edinburgh Mathematical Society, 1978