Abstract The weighted generalized cumulative residual entropy is a recently defined dispersion measure. This article introduces a new uncertainty measure as a generalization of the weighted generalized cumulative residual entropy, called it the weighted fractional generalized cumulative residual entropy of a nonnegative absolutely continuous random variable, which equates to the weighted fractional Shannon entropy. Several stochastic analyses and connections of this new measure to some famous stochastic orders are presented. As an application, we demonstrate this measure in random minima. The new measure can be used to study the coherent and mixed systems, risk measure, and image processing.

Abstract Inspired by the work Zhong et al. (2018), we study the linear tensor perturbation of both the flat and bent thick branes with inner structure in two-field mimetic gravity. The master equations for the linear tensor perturbations are derived by taking the transverse and traceless gauges. For the Minkowski and Anti-de-Sitter brane, the brane systems are stable against the tensor perturbation. The effective potentials of the tensor perturbations of both the flat and bent thick branes are volcano-like, and this structure may potentially lead to the zero-mode and the resonant modes of the tensor perturbation. We further illustrate the results of massive resonant modes.

Abstract In this work, we propose the Ritz approximation approach with a satisfier function to solve fractal-fractional advection–diffusion–reaction equations. The approach reduces fractal-fractional advection–diffusion–reaction equations to a system of algebraic equations; hence, the system can be solved easily to obtain the numerical solution for fractal-fractional advection–diffusion–reaction equations. With only a few terms of two variables-shifted Legendre polynomials, this method is capable of providing high-accuracy solution for fractal-fractional advection–diffusion–reaction equations. Numerical examples show that this approach is comparable with the existing numerical method. The proposed approach can reduce the number of terms of polynomials needed for numerical simulation to obtain the solution for fractal-fractional advection–diffusion–reaction equations.

Abstract This study sought to identify the most accurate forecasting models for COVID-19-confirmed cases, deaths, and recovered patients in Pakistan. For COVID-19, time series data are available from 16 April to 15 August 2021 from the Ministry of National Health Services Regulation and Coordination’s health advice portal. Descriptive as well as time series models, autoregressive integrated moving average, exponential smoothing models (Brown, Holt, and Winters), neural networks, and Error, Trend, Seasonal (ETS) models were applied. The analysis was carried out using the R coding language. The descriptive analysis shows that the average number of confirmed cases, COVID-19-related deaths, and recovered patients reported each day were 2,916, 69.43, and 2,772, respectively. The highest number of COVID-19 confirmed cases and fatalities per day, however, were recorded on April 17, 2021 and April 27, 2021, respectively. ETS (M, N, M), neural network, nonlinear autoregressive (NNAR) (3, 1, 2), and NNAR (8, 1, 4) forecasting models were found to be the best among all other competing models for the reported confirmed cases, deaths, and recovered patients, respectively. COVID-19-confirmed outbreaks, deaths, and recovered patients were predicted to rise on average by around 0.75, 5.08, and 19.11% daily. These statistical results will serve as a guide for disease management and control.

Abstract It is a well-known fact that functional effects like relaxation and retardation of materials, and heat transfer phenomena occur in a wide range of industrial and engineering problems. In this context, a mathematical model is developed in the view of Caputo fractional derivative for Oldroyd-B nano-fluid. Nano-sized particles of copper (Cu) are used to prepare nano-fluid taking water as the base fluid. The coupled non-linear governing equations of the problem are transformed into dimensionless form. Finite difference scheme is developed and applied successfully to get the numerical solutions of deliberated problem. Influence of different physical parameters on fluid velocity profile and temperature profile are analyzed briefly. It is observed that for increasing values of fractional parameter (α), fluid velocity increased, but opposite behavior was noticed for temperature profile. Nusselt number (Nu) decayed for advancement in values of heat source/sink parameter (Q 0), radiation parameter (Nr), volume fraction parameter of nano-fluid (ϕ), and viscous dissipation parameter (Ec). Skin friction (C f) boosts for the increase in the values of magnetic field parameter (Ha). It can also be noticed that the extended finite difference scheme is an efficient tool and gives the accurate results of discussed problem. It can be extended for more numerous type heat transfer problems arising in physical nature with complex geometry.

Abstract The radial motion of an electron in a Coulomb attracting field based on a new theory of the interaction of a particle with an electromagnetic field is studied. It is shown that the electron can perform radial oscillations due to a repulsive force that exists in the vicinity of the center and prevents the electron from approaching the center. This concept of a previously unknown repulsive force significantly shifts the paradigm of the interaction of a charge with an electromagnetic field. A laboratory experiment is proposed to test the new phenomenon.

Abstract The current work is devoted to introduce a novel thermoelastic heat conduction model where the Moore-Gibson-Thompson (MGT) equation describes the heat equation. The constructed model is characterized by allowing limited velocities of heat wave propagation within the material, consistent with physical phenomena. The Green–Naghdi Type III model is improved by introducing the delay factor into the modified Fourier law. Also, from the presented model, some other models of thermoelasticity can be derived at specific states. Based on the suggested model, an infinite orthotropic material with a cylindrical hole exposed to time-dependent temperature variation was studied. It has also been considered that the coefficient of thermal conductivity varies with temperature, unlike in many other cases where this value is considered constant. The viscoelastic material of the investigated medium was assumed to be of the Kelvin–Voigt type. The Laplace transform method provides general solutions to the studied field variables equations. The effects of viscosity and thermal variability parameters on these fields are discussed and graphically presented. In addition, the numerical results were presented in tables, and a comparison with previous models was made to ensure the accuracy of the results of the proposed model.

Abstract Light is a well-known electromagnetic wave that propagates, transmits, reflects, and polarizes in any medium. Waves have a huge technical impact as a determinant of human life because of their qualities. Using real geometrical Earth’s magnetic field, this article investigates the latitude and seasonal fluctuation of polarization magnitude of a polarized characteristic wave (no electric flux in the wave’s propagation direction) in the ionospheric plasma (the examined conditions). Both the volume polarization and wave polarization have been solved analytically in the ionospheric plasma, taking into account the accepted parameters. Furthermore, the volume and wave polarization were mathematically proven to be connected, and numerical wave polarization values were produced in the ionospheric plasma under the considered parameters. When a magnetic field operates on a medium, it causes the medium to become anisotropic. The wave polarization is ecliptic and the electric field vector does not sweep a circle as understood from analytical solutions when the Earth’s magnetic field and particle collisions are taken into account. There is a real and an imaginary element to the wave’s electric field ratio (E x /E y = a + ib). The real and imaginary parts of wave polarization in the x and y planes form the shape of the elliptic structure, and the real component is associated with advancing, while the imaginary part is related to attentiveness. The ionosphere of Earth, all physical parameters, such as refractive index, dielectric structure, and conductivity, have a complicated structure. According to the study, the real part of the polarization of the characteristic wave is related to the absorption coefficient and the imaginary part is proportional to the refractive index of the medium.

Abstract In controlling the angle error of laser profilometer contact measurement, the control model used in the past is subject to more external interference, which affects the measurement of other parameters, resulting in poor error control effect. Therefore, the angle error control model of laser profilometer contact measurement is designed by determining the initial zero position of the profilometer measuring sensor, compensating the non-linear error, designing the interference signal processing circuit, and avoiding the error measurement influenced by external factors. From the main error sources such as the perpendicularity, standard error, sensor error and other errors of the coordinate axis of the profilometer, the accuracy is distributed. According to the equal action principle, the measurement uncertainty of the profilometer is calculated, and the measurement is obtained. According to the interference signal processing circuit and measurement index, the serial communication control circuit is designed, and the angle error control model of laser profilometer contact measurement is constructed. The experimental results show that the designed laser profilometer contact measurement angle error control model has high precision and does not affect other parameters in the control process, which shows that the control model has good effect in practical application.

Abstract Kadomtsev–Petviashvili equation is used for describing the long water wave and small amplitude surface wave with weak nonlinearity, weak dispersion, and weak perturbation in fluid mechanics. Based on the modified symbolic computation approach, the multiple rogue wave solutions of a generalized (3+1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation are investigated. When the variable coefficient selects different functions, the dynamic properties of the derived solutions are displayed and analyzed by different three-dimensional graphics and contour graphics.