On variable-order fractional linear viscoelasticity

We discuss a generalisation of fractional linear viscoelasticity based on Scarpi's approach to variable-order fractional calculus. After reviewing the general mathematical framework, we introduce the variable-order fractional Maxwell model as a simple example for our analysis. We then provide some physical considerations for the fractionalisation procedure and on the choice of the transition functions. Lastly, we compute the material functions for the considered model and evaluate them numerically for exponential-type and Mittag-Leffler-type order functions.Comment: 14 pages, 17 figure

Beliefs and preferences regarding biological treatments for severe asthma

Background: Severe asthma is a serious condition with a significant burden on patients' morbidity, mortality, and quality of life. Some biological therapies targeting the IgE and interleukin-5 (IL5) mediated pathways are now available. Due to the lack of direct comparison studies, the choice of which medication to use varies. We aimed to explore the beliefs and practices in the use of biological therapies in severe asthma, hypothesizing that differences will occur depending on the prescribers’ specialty and experience. Methods: We conducted an online survey composed of 35 questions in English. The survey was circulated via the INterasma Scientific Network (INESNET) platform as well as through social media. Responses from allergists and pulmonologists, both those with experience of prescribing omalizumab with (OMA/IL5) and without (OMA) experience with anti-IL5 drugs, were compared. Results: Two hundred eighty-five (285) valid questionnaires from 37 countries were analyzed. Seventy-on percent (71%) of respondents prescribed biologics instead of oral glucocorticoids and believed that their side effects are inferior to those of Prednisone 5 mg daily. Agreement with ATS/ERS guidelines for identifying severe asthma patients was less than 50%. Specifically, significant differences were found comparing responses between allergists and pulmonologists (Chi-square test, p < 0.05) and between OMA/IL5 and OMA groups (p < 0.05). Conclusions: Uncertainties and inconsistencies regarding the use of biological medications have been shown. The accuracy of prescribers to correctly identify asthma severity, according to guidelines criteria, is quite poor. Although a substantial majority of prescribers believe that biological drugs are safer than low dose long-term treatment with oral steroids, and that they must be used instead of oral steroids, every effort should be made to further increase awareness. Efficacy as disease modifiers, biomarkers for selecting responsive patients, timing for outcomes evaluation, and checks need to be addressed by further research. Practices and beliefs regarding the use of asthma biologics differ between the prescriber's specialty and experience; however, the latter seems more significant in determining beliefs and behavior. Tailored educational measures are needed to ensure research results are better integrated in daily practice

Energy dissipation in viscoelastic Bessel media

We investigate the specific attenuation factor for the Bessel models of viscoelasticity. We find that the quality factor for this class can be expressed in terms of Kelvin functions and that its asymptotic behaviours confirm the analytical results found in previous studies for the rheological properties of these models

Scott-Blair models with time-varying viscosity

In a recent paper, Zhou et al. (2017) studied the time-dependent properties of Glass Fiber Reinforced Polymers composites by employing a new rheological model with a time-dependent viscosity coefficient. This rheological model is essentially based on a generalized Scott-Blair body with a time-dependent viscosity coefficient. Motivated by this study, in this note we suggest a different generalization of the Scott-Blair model based on the application of Caputo-type fractional derivatives of a function with respect to another function. This new mathematical approach can be useful in viscoelasticity and diffusion processes in order to model systems with time-dependent features. In this paper we also provide the general solution of the creep experiment for our improved Scott-Blair model together with some explicit examples and illuminating plots

A practical guide to Prabhakar fractional calculus

The Mittag-Leffler function is universally acclaimed as the Queen function of fractional calculus. The aim of this work is to survey the key results and applications emerging from the three-parameter generalization of this function, known as the Prabhakar function. Specifically, after reviewing key historical events that led to the discovery and modern development of this peculiar function, we discuss how the latter allows one to introduce an enhanced scheme for fractional calculus. Then, we summarize the progress in the application of this new general framework to physics and renewal processes. We also provide a collection of results on the numerical evaluation of the Prabhakar function