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In this paper, we provide solutions to the general fractional Caputo-type differential equation models for the dynamics of a sphere immersed in an incompressible viscous fluid and oscillatory process with fractional damping using Laplace transform method. We study the effects of fixing one of the fractional indices while varying the other as particular examples. We conclude this article by explaining the dynamics of the solutions of the models.

The emergence of higher-dimensional evolution equations in dissimilar scientific arenas has been on the rise recently with a vast concentration in optical fiber communications, shallow water waves, plasma physics, and fluid dynamics. Therefore, the present study deploys certain improved analytical methods to perform a solitonic analysis of the newly introduced three-dimensional nonlinear dynamical equations (all within the current year, 2024), which comprise the new (3 + 1) Kairat-II nonlinear equation, the latest (3 + 1) Kairat-X nonlinear equation, the new (3 + 1) Boussinesq type nonlinear equation, and the new (3 + 1) generalized nonlinear Korteweg–de Vries equation. Certainly, a solitonic analysis, or rather, the admittance of diverse solitonic solutions by these new models of interest, will greatly augment the findings at hand, which mainly deliberate on the satisfaction of the Painleve integrability property and the existence of solitonic structures using the classical Hirota method. Lastly, this study is relevant to contemporary research in many nonlinear scientific fields, like hyper-elasticity, material science, optical fibers, optics, and propagation of waves in nonlinear media, thereby unearthing several concealed features.

The dispersion of elastic shear waves in multilayered bodies is a topic of extensive research due to its significance in contemporary science and engineering. Anti-plane shear motion, a two-dimensional mathematical model in solid mechanics, effectively captures shear wave propagation in elastic bodies with relative mathematical simplicity. This study models the vibration of elastic waves in a multilayered inhomogeneous circular membrane using the Helmholtz equation with fractional-order infusion, effectively leveraging the anti-plane shear motion equation to avoid the computational complexity of universal plane motion equations. The method of the separation of variables and the conformable Bessel equation are utilized for the analytical examination of the model’s resulting vibrational displacements, as well as the dispersion relation. Additionally, the influence of various wave phenomena, including the dependencies of the wavenumber on the frequency and the phase speed on the wavenumber, respectively, with the variational effect of the fractional order on wave dispersion is considered. Numerical simulations of prototypical cases validate the formulated model, illustrating its applicability and effectiveness. The study reveals that fractional-order infusion significantly impacts the dispersion of elastic waves in both single- and multilayer membranes. The effects vary depending on the membrane’s structure and the wave propagation regime (long-wave vs. short-wave). These findings underscore the potential of fractional-order parameters in tailoring wave behavior for diverse scientific and engineering applications.

The present study analyzes the propagation of surface waves on a strongly inhomogeneous loaded bi-elastic cylindrical tube with variable material constituents. More precisely, due to the number of related physical applications, the exerted load is considered to be in favor of the Winkler elastic foundation. Further, analytical and approximation procedures of solution are beseeched to examine the model. The revealed results by two approaches are then graphically portrayed, which are then found to possess a high level of conformity. Finally, both the external load due to Winkler foundation d, and the internal material property b are found to oppose the propagation of surface waves in the media. In fact, the opposition deteriorates when both the dimensionless parameters d and b are greater than 0.5.

The present manuscript gives an overview of how two-dimensional heat diffusion models underwent a fractional transformation, system coupling as well as solution treatment. The governing diffusion models, which are endowed with Caputo's fractional-order derivatives in time t, are suitably coupled using the (1) convection phenomenon, (2) interfacial coupling by considering the mechanism of a double-layered bar, and the (3) nonlinear coupling due to temperature-dependent thermal diffusivities. Semi-analytical and analytical methods are considered for the solution treatment. Moreover, we seek a computational environment to graphically illustrate the systems' response to different fractional orders in each case through the determined diffusional fields. Besides, we supply certain concluding notes at the end.

The current manuscript critically examines the propagation of horizontally polarized shear waves on the dispersion of a highly inhomogeneous thin bonded bi-material plate when a load due to the Winkler's elastic foundation is prescribed. An analytical procedure of solution is deployed for the study; in addition to the exploitation of effective boundary conditions approach for the asymptotic examination. The overall inference of the current study is the realization of the fact that the vibrational displacements in both layers are enhanced by an increase in the inhomogeneity parameter; at the same time lessened with an increment in the foundation parameter. Moreover, a perfect approximation of the dispersion relation has been realized, with its validity extending to almost the entire low-frequency range. Lastly, the influence of the material inhomogeneity has been noted to affect fundamental mode, as against the presence of the foundation parameter which affects the first harmonic curve. More so, an increase in the two parameters narrows the chances of low-frequency propagation.

The present paper investigates the propagation and dispersion of elastic surface waves in an asymmetric inhomogeneous isotropic three-layered plate in the presence of magnetic field and rotational effects. The skin layers are exposed to an external magnetic field force while the core layer is assumed to be in a rotational frame of reference, which are perfectly bounded together with free-ends conditions. The resultant displacements and shear stresses in the respective layers are derived analytically together with the general dispersion relation. Further, the general dispersion relation is analyzed for some physical cases of interest. Finally, the effects of the magnetic field, rotation, and electric field on the propagation and dispersion of the present model are presented graphically. [ABSTRACT FROM AUTHOR]

The current study uses an essential and integrated form of Laplace-type integral transform coupled with the Adomian's approach to study nonlinear evolution equations endowed with non-integer derivatives. More so, of particular interest here is to demonstrate the application of this transform to a wider class of nonlinear problems. Three test models have been examined by the presented method, and their closed-form solutions have been reported iteratively. Lastly, the variational effect of the non-integer order derivatives on the evolution of these models has been studied via the two and three-dimensional depictions.

Growth of an epidemic is influenced by the natural variation in climatic conditions and enforcement variation in government stringency policies. Though these variations do not prompt an instant change in the growth of an epidemic, effects of climatic conditions and stringency policies become apparent over time. Time-lagged relationships and functional dynamic connectivity among meteorological covariates and stringency levels generate many lagged features deemed to be important for prediction of reproduction rate, a measure for growth of an epidemic. This empirical study examines the importance scores of lagged features and implements distributed lag inspired feature selection with back testing for model selection and forecasting. A verification forecasting scheme is developed for continuous monitoring of the growth of an epidemic. We have demonstrated the monitoring process by computing a week ahead expected target of the reproduction rate and then by computing a one day ahead verification forecast to evaluate the progress towards the expected target. This evaluation procedure will aid the analysts with a decision making tool for any early adjustment of control options to suppress the transmission.

The current manuscript examines the effect of the fractional temporal variation on the vibration of waves on non-homogeneous elastic substrates by applying the Laplace integral transform and the asymptotic approach. Four different non-homogeneities, including linear and exponential forms, are considered and scrutinized. In the end, it is reported that the fractional temporal variation significantly affects the respective vibrational fields greatly as the vibrations increase with a decrease in the fractional-order μ. Besides, the two approaches employed for the cylindrical substrates are also shown to be in good agreement for very small non-homogeneity parameter α. More so, the present study is set to play a vital role in the fields of material science, and non-homogenization processes to state a few.

The present manuscript examines the role of the Hilfer’s fractional operator on the evolution of three important linearized dynamical models of fluid dynamics. This fractional operator is very special since it interpolates between the two famous fractional derivative operators. The coupling of the Laplace integral transform and the Adomian’s decomposition method is adopted as the methodology. Lastly, the significance of the operator on the evolution of the models is demonstrated graphically for various values of the fractional-order α and type β.

The current study examines the propagation of surface waves in an asymmetric rotating doubly coated nonhomogeneous half space. The coating layers are assumed to be made of different homogeneous isotropic materials, while the overlaying nonhomogeneous half space layer is considered to be of exponentially varying material properties. The consequential exact vibrational displacements and dispersion relation are determined analytically, in addition to the approximate validation of the dispersion relation via the application of an asymptotic procedure within the long wave limit. Two cases of unloaded and loaded end surface scenarios are analyzed by examining the posed fundamental modes. More precisely, an elastic Winkler foundation was considered in the case of a mechanically loaded end surface condition and was found to proliferate the transition between having a fundamental mode over the frequency axis to the wave number axis as the angular velocity increased. Moreover, the rotational effect was found to have a direct impact on the surface wave propagation with a long wave and low frequency. Aside from that, an increase in the nonhomogeneity parameter resulted in propagation with a relatively long frequency.

The present manuscript focuses on the study of surface wave propagation in a rotating coated viscoelastic half-space and its response to external forces comprised of the magnetic field and gravitational forces. A celebrated normal mode analysis procedure is adopted as the methodology of interest for its high level of efficiency in the literature. The analytically obtained frequency equation is analyzed for certain scenarios of curiosity, in addition to the determination of the resulting displacements and stresses. Moreover, certain physical data of relevance with the viscoelasticity index of unity are considered for the numerical simulations. As for the findings, the presented graphical illustrations showed that both the magnetic field and rotation positively accelerated the dispersion of surface waves in the coated half-space, while the obtained approximate fields in the half-space are found to be oscillatory as they steadily move towards the limiting point.

Background: Clinical prediction rules (CPRs) can assist clinicians by focusing their clinical evaluation on the most important signs and symptoms, and if used properly can reduce the need for diagnostic testing. This study aims to perform an updated systematic review of clinical prediction rules and classification and regression tree (CART) models for the diagnosis of influenza., Methods: We searched PubMed, CINAHL, and EMBASE databases. We identified prospective studies of patients presenting with suspected influenza or respiratory infection and that reported a CPR in the form of a risk score or CART-based algorithm. Studies had to report at a minimum the percentage of patients in each risk group with influenza. Studies were evaluated for inclusion and data were extracted by reviewers working in parallel. Accuracy was summarized descriptively; where not reported by the authors the area under the receiver operating characteristic curve (AUROCC), predictive values, and likelihood ratios were calculated., Results: We identified 10 studies that presented 14 CPRs. The most commonly included predictor variables were cough, fever, chills and/or sweats, myalgias, and acute onset, all which can be ascertained by phone or telehealth visit. Most CPRs had an AUROCC between 0.7 and 0.8, indicating good discrimination. However, only 1 rule has undergone prospective external validation, with limited success. Data reporting by the original studies was in some cases inadequate to determine measures of accuracy., Conclusions: Well-designed validation studies, studies of interrater reliability between telehealth an in-person assessment, and studies using novel data mining and artificial intelligence strategies are needed to improve diagnosis of this common and important infection., Competing Interests: Conflict of interests: None., (© Copyright 2021 by the American Board of Family Medicine.)

Background: Seasonal influenza leads to significant morbidity and mortality. Rapid self-tests could improve access to influenza testing in community settings. We aimed to evaluate the diagnostic accuracy of a mobile app-guided influenza rapid self-test for adults with influenza like illness (ILI), and identify optimal methods for conducting accuracy studies for home-based assays for influenza and other respiratory viruses., Methods: This cross-sectional study recruited adults who self-reported ILI online. Participants downloaded a mobile app, which guided them through two low nasal swab self-samples. Participants tested the index swab using a lateral flow assay. Test accuracy results were compared to the reference swab tested in a research laboratory for influenza A/B using a molecular assay., Results: Analysis included 739 participants, 80% were 25-64 years of age, 79% female, and 73% white. Influenza positivity was 5.9% based on the laboratory reference test. Of those who started their test, 92% reported a self-test result. The sensitivity and specificity of participants' interpretation of the test result compared to the laboratory reference standard were 14% (95%CI 5-28%) and 90% (95%CI 87-92%), respectively., Conclusions: A mobile app facilitated study procedures to determine the accuracy of a home based test for influenza, however, test sensitivity was low. Recruiting individuals outside clinical settings who self-report ILI symptoms may lead to lower rates of influenza and/or less severe disease. Earlier identification of study subjects within 48 h of symptom onset through inclusion criteria and rapid shipping of tests or pre-positioning tests is needed to allow self-testing earlier in the course of illness, when viral load is higher.