We investigate the existence of multiple positive solutions to the nonlinear q-fractional boundary value problem c D a q u t a t f u t 0, 00, by using a fixed point theorem in a cone.

ObjectivesIn preterm infants, hyperbilirubinemia is common and can impair the central nervous system. The tests available for measuring bilirubin is to collect blood from heel pricking and occasionally taking blood samples from inserted cannulas, which is painful. Therefore, there is a need to develop a non-invasive device to detect bilirubin levels in newborns and interpret the severity of jaundice.MethodsWe conducted a cross-sectional study of 100 neonates. Patient data was collected between June 2015 and December 2016 from King Khalid Hospital at Al-Majma’ah, Saudi Arabia, and Alpine Hospital, Gurgaon, India. The mean gestational age of neonates was 39.0 weeks. Total bilirubin was measured using a transcutaneous bilirubinometer on the forehead and obtaining optical imaging through scanning of conjunctiva of eyes, also referred to as BiliChek and BiliCapture, respectively. Later the blood samples were obtained from these patients and tested in the laboratory to determine total serum bilirubin (TSB) levels.ResultsThe concentration of bilirubin as measured from serum, BiliChek, and BiliCapture were 10.7±2.0, 11.6±2.7, and 13.1±2.3 mg/dL, respectively. Correlation was high between TSB and BiliChek (r2 = 0.88) and between TSB and BiliCapture (r2 = 0.73). The Bland-Altman plots showed good agreement when comparing bilirubin values for both BiliChek and BiliCapture devices. Bilirubin measurement was further checked for the sensitivity and specificity and was 88.0% and 76.0% using BiliChek and 92.0% and 75.6% using BiliCapture, respectively.ConclusionsThe optical imaging of conjunctiva for bilirubin assay is a safe alternative to a laboratory bilirubin assay and transcutaneous bilirubinometer BiliChek.

The stochastic (2+1)-dimensional breaking soliton equation (SBSE) is considered in this article, which is forced by the Wiener process. To attain the analytical stochastic solutions such as the polynomials, hyperbolic and trigonometric functions of the SBSE, we use the tanh–coth method. The results provided here extended earlier results. In addition, we utilize Matlab tools to plot 2D and 3D graphs of analytical stochastic solutions derived here to show the effect of the Wiener process on the solutions of the breaking soliton equation.

This article considers the stochastic fractional Radhakrishnan-Kundu-Lakshmanan equation (SFRKLE), which is a higher order nonlinear Schrödinger equation with cubic nonlinear terms in Kerr law. To find novel elliptic, trigonometric, rational, and stochastic fractional solutions, the Jacobi elliptic function technique is applied. Due to the Radhakrishnan-Kundu-Lakshmanan equation’s importance in modeling the propagation of solitons along an optical fiber, the derived solutions are vital for characterizing a number of key physical processes. Additionally, to show the impact of multiplicative noise on these solutions, we employ MATLAB tools to present some of the collected solutions in 2D and 3D graphs. Finally, we demonstrate that multiplicative noise stabilizes the analytical solutions of SFRKLE at zero.

The space-fractional stochastic approximate long water wave equation (SFSALWWE) is considered in this work. The Riccati equation method is used to get analytical solutions of the SFSALWWE. This equation has never been examined with stochastic term and fractional space at the same time. In general, the noise term that preserves the symmetry reduces the domain of instability. To check the impact of Brownian motion on these solutions, we use a MATLAB package to plot 3D and 2D graphs for some analytical fractional stochastic solutions.

In this article, the stochastic Davey–Stewartson equations (SDSEs) forced by multiplicative noise are addressed. We use the mapping method to find new rational, elliptic, hyperbolic and trigonometric functions. In addition, we generalize some previously obtained results. Due to the significance of the Davey–Stewartson equations in plasma physics, nonlinear optics, hydrodynamics and other fields, the discovered solutions are useful in explaining a number of intriguing physical phenomena. By using MATLAB tools to simulate our results and display some of 3D graphs, we show how the multiplicative Brownian motion impacts the analytical solutions of the SDSEs. Finally, we demonstrate the effect of multiplicative Brownian motion on the stability and the symmetry of the achieved solutions of the SDSEs.

In this study, we take into account the fractional stochastic Kraenkel–Manna–Merle system (FSKMMS). The mapping approach may be used to produce various type of stochastic fractional solutions, such as elliptic, hyperbolic, and trigonometric functions. Solutions to the Kraenkel–Manna–Merle system equation, which explains the propagation of a magnetic field in a zero-conductivity ferromagnet, may provide insight into a variety of fascinating scientific phenomena. Moreover, we construct a variety of 3D and 2D graphics in MATLAB to illustrate the influence of the stochastic term and the conformable derivative on the exact solutions of the FSKMMS.

The stochastic Fokas system (SFS), driven by multiplicative noise in the Itô sense, was investigated in this study. Novel trigonometric, rational, hyperbolic, and elliptic stochastic solutions are found using a modified mapping method. Because the Fokas system is used to explain nonlinear pulse propagation in monomode optical fibers, the solutions provided may be utilized to analyze a broad range of critical physical phenomena. In order to explain the impacts of multiplicative noise, the dynamic performances of the different found solutions are illustrated using 3D and 2D curves. We conclude that multiplicative noise eliminates the symmetry of the solutions of the SFS and stabilizes them.