Exact solutions for the Cahn-Hilliard equation in terms of Weierstrass-elliptic and Jacobi-elliptic functions.

Despite the historical position of the F-expansion method as a method for acquiring exact solutions to nonlinear partial differential equations (PDEs), this study highlights its superiority over alternative auxiliary equation methods. The efficacy of this method is demonstrated through its application to solve the convective-diffusive Cahn-Hilliard (cdCH) equation, describing the dynamic of the separation phase for ternary iron alloys (Fe-Cr-Mo) and (Fe-X-Cu). Significantly, this research introduces an extensive collection of exact solutions by the auxiliary equation, comprising fifty-two distinct types. Six of these are associated with Weierstrass-elliptic function solutions, while the remaining solutions are expressed in Jacobi-elliptic functions. I think it is important to emphasize that, exercising caution regarding the statement of the term 'new,' the solutions presented in this context are not entirely unprecedented. The paper examines numerous examples to substantiate this perspective. Furthermore, the study broadens its scope to include soliton-like and trigonometric-function solutions as special cases. This underscores that the antecedently obtained outcomes through the recently specific cases encompassed within the more comprehensive scope of the present findings.

MHD rotating flow over a stretching surface: The role of viscosity and aggregation of nanoparticles.

The magnetohydrodynamic (MHD) rotating flow that occurs across a stretching surface has numerous practical applications in a variety of domains. These fields include astronomy, engineering, the material sciences, and space exploration. The combined examination of magnetohydrodynamics rotating flow across a stretching surface, taking into consideration fluctuating viscosity and nanoparticle aggregation, has significant ramifications across several different domains. It is essential for both the growth of technology and the attainment of deeper insights into the complicated fluid dynamics to maintain research in this field. Given the aforementioned motivation, the principal aim of this study is to examine the effects of variable viscosity on the bidirectional rotating magnetohydrodynamic flow over a stretching surface. Aggregation effects on nanoparticles are used in the analysis. Titania (TiO2) is taken nanoparticle and ethylene glycol as base fluid. The nonlinear ordinary differential equations and the boundary conditions that correspond to them can be transformed into a dimensionless form by using a technique called similarity transformation. To get a numerical solution to the transformed equation, the Runge-Kutta 4th order (RK-4) method is utilized, and this is done in conjunction with the shooting method. The impact of various leading variables on dimensionless velocity, the coefficients of temperature, skin friction and local Nusselt number are graphically represented. Velocity profiles in both direction increases with increasing values of φ. The Nusselt number increases with increasing values of the radiation and temperature ratio parameters. When a 1 % volume fraction of nanoparticles is introduced, the Nusselt number exhibits a 0.174 % increase for the aggregation model compared to the regular fluid in the absence of radiation effects. When the aggregation model is used with a 1 % volume fraction of nanoparticles, the skin friction increases by 0.1153 % in the x direction and by 0.1165 % in the y direction compared to the regular fluid. Tables show the variation in Nusselt numbers, as well as a comparison of the effects of nanoparticle's aggregation model without and with radiation. Moreover, the numerical results obtained were compared with previously published data, demonstrating a satisfactory agreement. We firmly believe that this finding will have extensive implications for engineering and various industries.

Predictive dynamical modeling and stability of the equilibria in a discrete fractional difference COVID-19 epidemic model.

The SARSCoV-2 virus, also known as the coronavirus-2, is the consequence of COVID-19, a severe acute respiratory syndrome. Droplets from an infectious individual are how the pathogen is transmitted from one individual to another and occasionally, these particles can contain toxic textures that could also serve as an entry point for the pathogen. We formed a discrete fractional-order COVID-19 framework for this investigation using information and inferences from Thailand. To combat the illnesses, the region has implemented mandatory vaccination, interpersonal stratification and mask distribution programs. As a result, we divided the vulnerable people into two groups: those who support the initiatives and those who do not take the influence regulations seriously. We analyze endemic problems and common data while demonstrating the threshold evolution defined by the fundamental reproductive quantity R 0 . Employing the mean general interval, we have evaluated the configuration value systems in our framework. Such a framework has been shown to be adaptable to changing pathogen populations over time. The Picard Lindelöf technique is applied to determine the existence-uniqueness of the solution for the proposed scheme. In light of the relationship between the R 0 and the consistency of the fixed points in this framework, several theoretical conclusions are made. Numerous numerical simulations are conducted to validate the outcome.