The nanofluid flow under the consequences of Brownian motion, thermophoresis, and nonlinear radiation has been numerically studied over a heated rotating disc. Arrhenius activation energy is used to describe the various aspects of heat and mass transition. The problem has been modeled in the form of a system of PDEs consist of the Maxwell and Navier Stokes equations. The system of modeled equations has been reduced to the ordinary system of dimensionless differential equations using a similarity framework. For the problem's quantitative approximation, the results have been obtained through numerical technique boundary value solver (bvp4c). The physical quantities that derive from the modeled equations are displayed and addressed. It has been perceived that the Prandtl number and radiation effect improves the heat transmission rate while improving the magnetic parameter reduces the velocity field. Furthermore, the entropy rate and Bejan number increases with the rising effect of chemical reaction, temperature differential variable, concentration ratio variable and Schmidt number.

We explore stochastic–fractional Drinfel’d–Sokolov–Wilson (SFDSW) equations for some wave solutions such as the cross-kink rational wave solution, periodic cross-rational wave solution and homoclinic breather wave solution. We also examine some M-shaped solutions such as the M-shaped rational solution, M-shaped rational solution with one and two kink waves. We also derive the M-shaped interaction with rogue and kink waves and the M-shaped interaction with periodic and kink waves. This model is used in mathematical physics, surface physics, plasma physics, population dynamics and applied sciences. Moreover, we also show our results graphically in different dimensions. We obtain these solutions under some constraint conditions.

This research investigates the influence of the combined effect of the chemically reactive and thermal radiation on electrically conductive stagnation point flow of nanofluid flow in the presence of a stationary magnetic field. Furthermore, the effect of Newtonian heating, thermal dissipation, and activation energy are considered. The boundary layer theory developed the constitutive partial differential momentum, energy, and diffusion balance equations. The fundamental flow model is changed to a system of coupled ordinary differential equations (ODEs) via proper transformations. These nonlinear-coupled equations are addressed analytically by implementing an efficient analytical method, in which a Mathematica 11.0 programming code is developed for numerical simulation. For optimizing system accuracy, stability and convergence analyses are carried out. The consequences of dimensionless parameters on flow fields are investigated to gain insight into the physical parameters. The result of these physical constraints on momentum and thermal boundary layers, along with concentration profiles, are discussed and demonstrated via plotted graphs. The computational outcomes of skin friction coefficient, mass, and heat transfer rate under the influence of appropriate parameters are demonstrated graphically.

In this work, we investigate the oscillatory properties of the neutral differential equation ${(r(l){\left[{(s(l)+p(l)s(g(l)))}^{\prime }\right]}^{\mathfrak{v}})}^{\prime }+{\sum }_{i=1}^n{q}_i(l)s^{\mathfrak{v}}(h_i(l))=0$, where $s\ge s_0$. We first present new monotonic properties for the solutions of this equation, and these properties are characterized by an iterative nature. Using these new properties, we obtain new oscillation conditions that guarantee that all solutions are oscillate. Our results are a complement and extension to the relevant results in the literature. We test the significance of the results by applying them to special cases of the studied equation.