Razumikhin Stability Theorem for Fractional Systems with Delay

Fractional calculus techniques and methods started to be applied successfully during the last decades in several fields of science and engineering. In this paper we studied the stability of fractional-order nonlinear time-delay systems for Riemann-Liouville and Caputo derivatives and we extended Razumikhin theorem for the fractional nonlinear time-delay systems

Estimation of the light field inside photosynthetic microorganism cultures through Mittag-Leffler functions at depleted light conditions

[EN] Light attenuation within suspensions of photosynthetic microorganisms has been widely described by the Lambert-Beer equation. However, at depths where most of the light has been absorbed by the cells, light decay deviates from the exponential behaviour and shows a lower attenuation than the corresponding from the purely exponential fall. This discrepancy can be modelled through the Mittag-Leffler function, extending Lambert-Beer law via a tuning parameter ¿ that takes into account the attenuation process. In this work, we describe a fractional Lambert-Beer law to estimate light attenuation within cultures of model organism Synechocystis sp. PCC 6803. Indeed, we benchmark the measured light field inside cultures of two different Synechocystis strains, namely the wild-type and the antenna mutant strain called Olive at five different cell densities, with our in silico results. The Mittag-Leffler hyper-parameter ¿ that best fits the data is 0.995, close to the exponential case. One of the most striking results to emerge from this work is that unlike prior literature on the subject, this one provides experimental evidence on the validity of fractional calculus for determining the light field. We show that by applying the fractional Lambert-Beer law for describing light attenuation, we are able to properly model light decay in photosynthetic microorganisms suspensions.This project has received funding from the European Unions Seventh Programme for Research, technological development and demonstration under grant agreement No 308518 CyanoFactory. David Fuente is supported by grant Contratos Predoctorales FPI 2013 of the Universitat Politecnica de Valencia. Carlos Lizama is supported by Programa de Apoyo a la Investigation y Desarrollo (PAID-02-15) de la Universitat Politecnica de Valencia and CONICYT - PIA - Anillo ACT1416Fuente, D.; Lizama, C.; Urchueguía Schölzel, JF.; Conejero, JA. (2018). Estimation of the light field inside photosynthetic microorganism cultures through Mittag-Leffler functions at depleted light conditions. Journal of Quantitative Spectroscopy and Radiative Transfer. 204:23-26. https://doi.org/10.1016/j.jqsrt.2017.08.012S232620

On the existence of fixed points that belong to the zero set of a certain function

Let T : X -> X be a given operator and F-T be the set of its fixed points. For a certain function phi : X -> [0,infinity), we say that F-T is phi-admissible if F-T is nonempty and F-T subset of Z(phi), where Z(phi) is the zero set of phi. In this paper, we study the phi-admissibility of a new class of operators. As applications, we establish a new homotopy result and we obtain a partial metric version of the Boyd-Wong fixed point theorem