In this paper, we study human liver disease with a different approach of interval-based investigation by introducing subintervals. This investigation may be referred to as a short memory investigation. Such concepts are useful in problems where a transition is observed when transitioning from one subinterval to the other one. We use the classical and fractal-fractional-order derivative in each subinterval. We study the existence of solutions by using Banach’s and Krasnoselskii’s fixed-point theorems. Their stability is analyzed by adopting the Hyers–Ulam (H-U) stability approach. Also, using the extended Adams–Bashforth–Moulton (ABM) method, we simulate the results that visually present the numerical solutions for different fractal-fractional-order values.

This paper investigates the explicit, accurate soliton and dynamic strategies in the resolution of the Wazwaz–Benjamin–Bona–Mahony (WBBM) equations. By exploiting the ensuing wave events, these equations find applications in fluid dynamics, ocean engineering, water wave mechanics, and scientific inquiry. The two main goals of the study are as follows: Firstly, using the dynamic perspective, examine the chaos, bifurcation, Lyapunov spectrum, Poincaré section, return map, power spectrum, sensitivity, fractal dimension, and other properties of the governing equation. Secondly, we use a generalized rational exponential function (GREF) technique to provide a large number of analytical solutions to nonlinear partial differential equations (NLPDEs) that have periodic, trigonometric, and hyperbolic properties. We examining the wave phenomena using 2D and 3D diagrams along with a projection of contour plots. Through the use of the computational program Mathematica, the research confirms the computed solutions to the WBBM equations.

This research article investigates a tripled system of nonlinear fractional differential equations with n terms. The study explores this novel class of differential equations to establish existence and stability results. Utilizing Schaefer’s and Banach’s fixed point theorems, we derive sufficient conditions for the existence of at least one solution, as well as a unique solution. Furthermore, we apply Hyers–Ulam stability analysis to establish criteria for the stability of the system. To demonstrate the applicability of the main results, a detailed example is provided.

This study explores the novel dynamics of the (3+1)-dimensional generalized Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation. A Galilean transformation is employed to derive the associated system of equations. Perturbing this system allows us to investigate the presence and characteristics of chaotic behavior, including return maps, fractal dimension, power spectrum, recurrence plots, and strange attractors, supported by 2D and time-dependent phase portraits. A sensitivity analysis is demonstrated to show how the system behaves when there are small changes in initial values. Finally, the planar dynamical system method is used to derive anti-kink, dark soliton, and kink soliton solutions, advancing our understanding of the range of solutions admitted by the model.

This article implements the Hirota bilinear (HB) transformation technique to the Landau–Ginzburg–Higgs (LGH) model to explore the nonlinear evolution behavior of the equation, which describes drift cyclotron waves in superconductivity. Utilizing the Cole–Hopf transform, the HB equation is derived, and symbolic manipulation combined with various auxiliary functions (AFs) are employed to uncover a diverse set of analytical solutions. The study reveals novel results, including multi-wave complexitons, breather waves, rogue waves, periodic lump solutions, and their interaction phenomena. Additionally, a range of traveling wave solutions, such as dark, bright, periodic waves, and kink soliton solutions, are developed using an efficient expansion technique. The nonlinear dynamics of these solutions are illustrated through 3D and contour maps, accompanied by detailed explanations of their physical characteristics.

To investigate the existence of bovine viral diarrhoea virus (BVDV), parainfluenza virus 3 (PIV-3) and respiratory syncytial virus (RSV) as well as its coinfections, a total of 420 pneumonic lung tissue samples were collected from slaughterhouses in three different areas. Samples were examined for the three viruses using antigen detection enzyme-linked immunosorbent assay (ELISA) test, and positive results were further confirmed using fluorescent antibody test and polymerase chain reaction. Prevalences detected were 10.47% for BVDV, 11.9% for parainfluenza virus type (PIV-3) and 7.6% for respiratory syncytial virus (RSV). Observed coinfections were bovine viral diarrhoea (BVD) and PIV-3 in 8.1%, BVD and RSV in only two samples (1%). Existence of all three viruses was detected in two samples (1%). Contribution: In this study, infection of the three viruses was confirmed in cattle and existence of its coinfection is documented for the first time.