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The paper is designed to highlight the presence of an optimal solution to a differential system comprising fractional order derivatives, precisely the ψ-Caputo derivative, under the prescribed initial constraints. This is attained through a new variant of cyclic (noncyclic) condensing operators incorporating a pair of maps. The altered notion facilitates in evolving best proximity point (pair) results as well as coupled best proximity point results with supportive corollaries. [ABSTRACT FROM AUTHOR]

This work intends to treat the existence of mild solutions for the Hilfer fractional hybrid differential equation (HFHDE) with linear perturbation of first and second type in partially ordered Banach spaces. First, we establish the results concerning the actuality of fixed point of sum and product of operators via the concepts of measure of noncompactness and simulation functions in partially ordered spaces. Then combining these fixed point theorems with the concepts in fractional calculus, new existence results for mild solutions of HFHDE’s are established. Furthermore, the presented fixed point results and existence results improve and extend the present state-of-art in the literature. Competent examples in support of theory are illustrated for better understanding.

In the present study, we establish the existence and uniqueness of solutions for nonlinear initial value problems and nonlocal boundary value problems associated with implicit fractional differential equations involving k,Ψ$$ \left(k,\Psi \right) $$‐Hilfer derivative operator. Furthermore, we explore the stability properties of these solutions in the sense of the Ulam–Hyers, Ulam–Hyers–Rassias, and their generalized stability concepts by proving and applying generalized Gronwall inequality. Lastly, we present the fractional RC$$ \mathcal{RC} $$ electric circuit model as an example to show the practical applicability of our main results. [ABSTRACT FROM AUTHOR]

The notion of A -condensing operators via the measure of noncompactness is proposed, which retains the existing classes of condensing operators. Results concerning the existence of the best proximity point (pair) of cyclic (noncyclic) A -condensing operators along with the coupled best proximity-point theorem for cyclic A -condensing operators have been formulated. An application to a (k , ℷ) -Hilfer fractional differential equation of order 2 < p < 3 , type q ∈ [ 0 , 1 ] satistfying some boundary conditions is presented. The paper is the first to investigate the optimum solution of such a generalized fractional differential equation. The hypothesis involved in the investigation is independent of the incorporated measure of noncompactness, thereby making our result better in application than that present in the literature. Moreover, added numerical examples validate the theoretical conclusions. [ABSTRACT FROM AUTHOR]

Primarily this work intends to investigate the existence of best proximity points (pairs) for new classes of cyclic (noncyclic) mappings via simulation functions and measure of noncompactness. Use of different classes of additional functions make it possible to generalize the contractive inequalities in this work. As an application of the main conclusions, a survey for the existence of optimal solutions of a system of integro-differential equations under some new conditions is presented. As an application of our existence results, we establish the existence of a solution for the following system of integro-differential equations {(u'(t) = F1(t,u(t), ∫t0t k1(t,s,u(s))ds), u(t0) = u1, v'(t) = F2(t,v(t), ∫t0t k2(t,s,v(s))ds), v(t0) = u2, in the space of all bounded and continuous real functions on [0, + ∞) under suitable assumptions on F1, F2. [ABSTRACT FROM AUTHOR]

A new proper generalization of metric called as θ -metric is introduced by Khojasteh et al. (Mathematical Problems in Engineering (2013) Article ID 504609). In this paper, first we prove the Caristi type fixed point theorem in an alternative and comparatively new way in the context of θ -metric. We also investigate two θ -metrics on CB (X) (family of nonempty closed and bounded subsets of a set X). Furthermore, using the obtained θ -metrics on CB (X) , we prove two new fixed point results for multi-functions which generalize the results of Nadler and Lim type in the context of such spaces. In order to illustrate the usability of our results, we equipped them with competent examples. [ABSTRACT FROM AUTHOR]

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) continues its largely aseasonal spread with millions of cases per year. Highly sensitive, point-of-care testing is critical for rapid detection of coronavirus disease 2019 (COVID-19) cases and initiation of antiviral therapy to avert adverse health outcomes and reduce onward transmission of the virus. While hundreds of COVID-19 diagnostics received emergency use authorization from the FDA during the pandemic, significantly fewer have navigated the course to FDA clearance or approval. Here, we determined the clinical performance of the Cepheid Xpert Xpress CoV-2 plus for detection of SARS-CoV-2 in 3,750 anterior nasal swab (NS) specimens and nasopharyngeal swab (NPS) from 32 sites in comparison to the FDA-authorized BioFire Respiratory Panel 2.1. Three-quarters of specimens collected were tested on the Xpert Xpress CoV-2 plus in the point-of-care setting. Overall positive percent agreement (PPA) was 98.1% (95% CI: 96.7%-98.9%) and negative percent agreement (NPA) was 98.3% (97.7%-98.7%). Performance of the Xpert Xpress CoV-2 plus was slightly improved in NS compared to NPS specimens, with PPA of 99.3% versus 97.0% (Fisher's exact test, P = 0.06) and NPA of 98.3% versus 98.2% ( P = 0.89), respectively. Assay PPA was similar between untrained and trained users (98.7% vs 97.3%, P = 0.75), while NPA was slightly improved for untrained users (99.0% vs 97.6%, P = 0.0003). This study showed that Cepheid Xpert Xpress COV-2 plus is highly sensitive and specific/has high PPA and NPA for detection of SARS-CoV-2 from both NS and NPS specimens., Importance: Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) continues to cause millions of infections and tens of thousands of deaths per year in the United States. While the FDA authorized hundreds of SARS-CoV-2 tests during the public health emergency, significantly fewer have made the transition to being cleared or approved. There continues to be a need for FDA-authorized point-of-care SARS-CoV-2 testing that can be performed by untrained users. We conducted a large prospective study of the Cepheid Xpert Xpress CoV-2 plus test for detection of SARS-CoV-2 in both nasal and nasopharyngeal swabs by trained and untrained users. The assay demonstrated excellent clinical performance characteristics and, as a result of this study, was cleared by the FDA., Competing Interests: This study was supported by Cepheid. A.L.G. reports contract testing from Abbott, Novavax, Pfizer, Janssen, and Hologic, as well as research support from Gilead, outside of the described work. D.R., X.L., and A.R. are employees of Cepheid.

Background: Liver diseases continue to destroy the lives of people, one of which is known as Non-alcoholic Steatohepatitis (NASH) that becomes a serious liver disease all around the world over the last few years. Non-alcoholic Steatohepatitis (NASH) is a progressive form of Nonalcoholic Fatty Liver Disease (NAFLD) and is characterized by liver steatosis, inflammation, different degrees of fibrosis, and hepatocellular injury. The inflammatory mediators play a vital role in the transition of Non-alcoholic Fatty Liver (NAFL) to Non-alcoholic Steatohepatitis (NASH), which further leads to Hepatocellular Carcinoma (HCC) and becomes a cause of liver transplantation., Objectives: Considering the severity and complexity of the disease, we aim to summarize the works of various research groups that are working in the area of NASH to find a sophisticated treatment., Results: The present review focused on various factors that are responsible for the development and progression of this prevalent disease, emerging pharmacotherapies as well as therapeutic targets that have been utilized for the treatment of NASH. We also have conducted the structural analysis of available targets, which will be helpful for the enhancement of drug discovery through the implementation of in silico methods., Conclusion: Efforts have been made to provide an update on research in the area of NASH, including the pharmacological agents that are currently undergoing clinical trials for the treatment of NASH. Besides the massive research, still, gaps and challenges are there in the drug development for NASH that also have been discussed., (Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.net.)