In this article, we utilize the conformable fractional (CF) derivative to investigate the analytically innovative soliton solutions for the time‐fractional nonlinear perturbed Chen‐Lee‐Liu (CLL) equation in optical fibers. An essential governing equation in nonlinear optics, the perturbed CLL model describes the propagation of ultrashort pulses in optical fibers with higher‐order perturbations, and its study is critical to the development of high‐capacity optical communication systems. Several types of optical soliton solutions for this model with a conformable derivative are extracted in this study by using the modified Khater method and the modified ‐expansion approach. The obtained bright, dark, periodic, and kink soliton solutions offer important information for developing and regulating new optical devices, including all‐optical switches and soliton‐based data transmitters. The significant impact of the CF derivative on the soliton dynamics and symmetric features of the resulting solutions is demonstrated by two‐ and three‐dimensional graphical representations created with MATLAB software. Moreover, stability, sensitivity, and chaotic are successfully analyzed through diverse values of unknown parameters.

Rumor propagation significantly impacts both individual well‐being and societal stability, with various factors influencing its spread. While existing research has primarily focused on the role of interpersonal familiarity in rumor diffusion, this study introduces a different perspective: an individual’s familiarity with the subject matter itself plays a crucial role in the dissemination process. To explore this, we develop a novel rumor‐spreading model that explicitly accounts for subject‐matter familiarity. A rigorous theoretical analysis is conducted to assess the existence and stability of equilibrium points, and we derive the system’s basic reproduction number. Through numerical simulations, we systematically investigate how key parameters affect rumor dynamics. Our results confirm that subject‐matter familiarity is a significant driver of rumor spread, supporting our initial assumption. Additionally, we identify three key control variables and demonstrate that optimizing these factors enhances the effectiveness of rumor suppression. Based on these findings, we propose practical strategies for managing and mitigating rumor dissemination.

This study investigates characteristics of the mass transport for Maxwell fluids driven by a time‐periodic oscillatory electroosmotic flow (EOF) in annular microchannels under high zeta potential conditions. A finite difference method is employed to solve the nonlinear Poisson–Boltzmann equation, the Maxwell fluid momentum equation, the convection–diffusion equation, and the time‐ and space‐averaged mass transport rates are obtained by using the composite trapezoidal rules, and the reliability of the present numerical results for the low zeta potential is verified by comparing the analytical approximate results obtained by using the Debye–Hückel (D–H) linear approximation. The effects of key dimensionless parameters—including electrokinetic width, angular Reynolds number, wall potential ratio, relaxation time, and the inner‐to‐outer radius ratio—on flow velocity, solute concentration distribution, and average mass transport performance are systematically analyzed. The results show that: (1) a high zeta potential enhances velocity and concentration, while suppressing the spatio‐temporal average mass transport rate; (2) the elastic effects of Maxwell fluids, characterized by relaxation time, significantly modulate the structure of velocity and concentration fields under periodic electric forcing, thereby enhancing local mixing or enabling spatially selective separation; (3) at low Reynolds number, the flow remains relatively uniform, facilitating species separation, whereas at higher Reynolds number, amplified elastic responses near the walls lead to increased nonuniformity in velocity and concentration distributions, promoting mixing; (4) asymmetric zeta potentials induce elastic responses in the core region, further intensifying concentration nonuniformity and enabling species separation under specific parameter combinations; and (5) geometric factors such inner‐to‐outer radius ratio and electrokinetic width significantly affect radial gradient intensity, resulting in switching phenomena between fast‐ and slow‐diffusing species.

The problem of normal incidence of a plane wave on a layer with a one‐dimensional perturbation of the permittivity of the medium is considered under the condition that the spatial scale of the inhomogeneity can be both much smaller and on the order of the wavelength in vacuum. An estimate is obtained for the deviation of the solution corresponding to the short‐wavelength approximation from the rigorous solution of the wave equation. The conditions for applying the expression for the field corresponding to the geometric‐optical approach are determined in the case of commensurability of the wavelength and the spatial scale of the inhomogeneity.

The effect of an imposed alternating current (A.C) electric field on the onset of convective instability in a horizontal triply diffusive fluid layer is investigated. Analytical solutions are obtained for steady and oscillatory onset when imposed gradients of the stratifying agencies are constant and vertical. It was found that A.C electric Rayleigh number did not affect the necessary conditions for oscillatory convection. The stability boundaries are drawn and it is observed that an increase in the A.C electric field strength is to hasten the onset of convection. The evolution of neutral curves is analyzed in detail by varying the A.C electric Rayleigh number and other physical parameters. For certain choices of physical parameters, it is noted that the oscillatory part will give rise to two oscillatory neutral solutions for each wave number and closed disconnected neutral curves are found to exist, suggesting the requirement for three critical Rayleigh numbers to specify the linear stability criterion.

In this article, we study and introduce the Marshall–Olkin extended exponential (MO‐ExE) distribution, a novel three‐parameter life expectancy distribution. The new model is characterized by high adaptability in data analysis. Various mathematical properties, including ordinary moments, moment‐generating functions (MGFs), and conditional moments (CMs) of the new suggested model, were computed. The model parameters are estimated using the maximum likelihood method. A simulation study is evaluated to demonstrate the behavior of the parameter model. In the final analysis, we demonstrate the significance of the novel model by examining practical data applications, thus, showing the adaptability and potential of the MO‐ExE model.

The strong, transient working conditions where heat transfer involves extremely large temperature gradients, extremely large heat fluxes, and extremely short time durations of thermal disturbances may occur in engineering materials and structures. Fourier heat conduction assumes heat propagation at an infinite speed, which is not suitable for strong, transient thermal working conditions. In this paper, a Newmark integral method is presented to deal with the strong, transient heat conduction in nonhomogeneous materials based on the hyperbolic heat conduction theory. The second‐order differential equation of the strong transient temperature field is discretized in the spatial and temporal domains through the finite element method (FEM) and the Newmark integral method, respectively. This allows them to be solved directly without the necessity to convert them into a pair of first‐order differential equations using the Newmark integral method. Several test examples are presented to demonstrate the application of the current method. Firstly, the stability of the Newmark integral method is analyzed to ensure that the numerical oscillation is suppressed in the calculation. Then the time‐related temperature field of functionally graded material (FGM) plate under strong transient thermal shock is analyzed. Finally, the thermal stress intensity factors (TSIFs) in an FGM plate with parallel cracks are extracted after combining with interaction energy integral methods (IEIMs). The results confirm that the Newmark integral method can efficiently address the transient thermal problem and ensure stability. The temperature overshooting phenomenon and thermal wave singularity are visualized at the finite speed of heat propagation. Moreover, the numerical results agree well with analytical solutions. The current method can be well applied to the design and evaluation of thermal protective materials in extreme thermal environments.

This study presents an analytical solution to the fractional wave equation incorporating the Riesz fractional derivative (RFD) of the form (−Δ)γ/2, where 0 < γ ≤ 2 is the order of RFD. The equation is formulated within a fractional‐dimensional spatial domain, with the dimension d constrained to the interval 2 < d ≤ 3. The solution methodology is based on the fractional Fourier transform technique (FFTT) developed by Muslih and Agrawal. Solutions are derived in closed form using Fox H‐functions (FHFs), represented through their Mellin–Barnes integral formulations. The analysis confirms the existence of valid solutions for all admissible values of γ in the range (0, 2].

The purpose of the study is to investigate the thermal proficiency of a trihybrid magnetized water‐based cross nanofluid over an inclined shrinking sheet. Cross‐fluid is the best model to investigate the fluid flow at a very high and very low share rate. There are three nanoparticles that are added in based fluid (water) to form the requisite posited ternary hybrid nanofluid. Moreover, heat transport analysis is scrutinized by incorporating the melting conditions. The obtained nonlinear system of partial differential equations (PDEs) from assumed physical assumption is converted into the nonlinear setup of ordinary differential equations (ODEs). These ODEs are passed under the boundary value problem of a fourth‐order (bvp4c) MATLAB program for numerical results. With the help of bvp4c, data are further trained through an artificial neural network and results are predicted. Results are compared with both techniques and found smooth agreement. The obtained numerical results provide valuable insight for optimizing heat transfer processes involving nanoparticle‐enhanced fluid on inclined shrinking sheets. From the results, it is concluded that the inclusion of nanoparticles enhances the viscosity and thermal conductivity of the fluid. High temperatures make rapid heat transfer scenarios.