Bright-Dark and Multi Solitons Solutions of (3 + 1)-Dimensional Cubic-Quintic Complex Ginzburg-Landau Dynamical Equation with Applications and Stability.

In this paper, bright-dark, multi solitons, and other solutions of a (3 + 1)-dimensional cubic-quintic complex Ginzburg-Landau (CQCGL) dynamical equation are constructed via employing three proposed mathematical techniques. The propagation of ultrashort optical solitons in optical fiber is modeled by this equation. The complex Ginzburg-Landau equation with broken phase symmetry has strict positive space-time entropy for an open set of parameter values.

Investigation of Entropy in Two-Dimensional Peristaltic Flow with Temperature Dependent Viscosity, Thermal and Electrical Conductivity.

This study comprehensively explores the generalized form of two-dimensional peristaltic motions of incompressible fluid through temperature-dependent physical properties in a non-symmetric channel. Generation of entropy in the system, carrying Joule heat and Lorentz force is also examined. Viscous dissipation is not ignored, for viewing in-depth, effects of heat transmission and entropy production.

MHD flow of Maxwell fluid with nanomaterials due to an exponentially stretching surface.

In many industrial products stretching surfaces and magnetohydrodynamics are being used. The purpose of this article is to analyze magnetohydrodynamics (MHD) non-Newtonian Maxwell fluid with nanomaterials in a surface which is stretching exponentially. Thermophoretic and Brownian motion effects are incorporated using Buongiorno model.

Explicit Lump Solitary Wave of Certain Interesting (3+1)-Dimensional Waves in Physics via Some Recent Traveling Wave Methods.

This study investigates the solitary wave solutions of the nonlinear fractional Jimbo-Miwa (JM) equation by using the conformable fractional derivative and some other distinct analytical techniques. The JM equation describes the certain interesting (3+1)-dimensional waves in physics. Moreover, it is considered as a second equation of the famous Painlev'e hierarchy of integrable systems.

Analysis and Optimal Control of Fractional-Order Transmission of a Respiratory Epidemic Model.

The World Health Organization is yet to realise the global aim of achieving future-free and eliminating the transmission of respiratory diseases such as H1N1, SARS and Ebola since the recent reemergence of Ebola in the Democratic Republic of Congo. In this paper, a Caputo fractional-order derivative is applied to a system of non-integer order differential equation to model the transmission dynamics of respiratory diseases. The nonnegative solutions of the system are obtained by using the Generalized Mean Value Theorem.

Entropy Analysis of 3D Non-Newtonian MHD Nanofluid Flow with Nonlinear Thermal Radiation Past over Exponential Stretched Surface.

The present study characterizes the flow of three-dimensional viscoelastic magnetohydrodynamic (MHD) nanofluids flow with entropy generation analysis past an exponentially permeable stretched surface with simultaneous impacts of chemical reaction and heat generation/absorption. The analysis was conducted with additional effects nonlinear thermal radiation and convective heat and mass boundary conditions. Apposite transformations were considered to transform the presented mathematical model to a system of differential equations.

A numerical treatment of MHD radiative flow of Micropolar nanofluid with homogeneous-heterogeneous reactions past a nonlinear stretched surface.

The impact of nonlinear thermal radiation in the flow of micropolar nanofluid past a nonlinear vertically stretching surface is investigated. The electrically conducting fluid is under the influence of magnetohydrodynamics, heat generation/absorption and mixed convection in the presence of convective boundary condition. The system of differential equations is solved numerically using the bvp4c function of MATLAB.

Nonlinear radiation effect on MHD Carreau nanofluid flow over a radially stretching surface with zero mass flux at the surface.

A mathematical model is envisaged to study the axisymmetric steady magnetohydrodynamic (MHD) Carreau nanofluid flow under the influence of nonlinear thermal radiation and chemical reaction past a radially stretched surface. Impact of heat generation/absorption with newly introduced zero mass flux condition of nanoparticles at the sheet is an added feature towards novelty of the problem. Further, for nanofluid the most recently organized model namely Buongiorno's model is assumed that comprises the effects thermophoresis and Brownian motion.

A numerical treatment of radiative nanofluid 3D flow containing gyrotactic microorganism with anisotropic slip, binary chemical reaction and activation energy.

A numerical investigation of steady three dimensional nanofluid flow carrying effects of gyrotactic microorganism with anisotropic slip condition along a moving plate near a stagnation point is conducted. Additionally, influences of Arrhenius activation energy, joule heating accompanying binary chemical reaction and viscous dissipation are also taken into account. A system of nonlinear differential equations obtained from boundary layer partial differential equations is found by utilization of apposite transformations.

Buoyancy effects on the radiative magneto Micropolar nanofluid flow with double stratification, activation energy and binary chemical reaction.

A mathematical model has been developed to examine the magneto hydrodynamic micropolar nanofluid flow with buoyancy effects. Flow analysis is carried out in the presence of nonlinear thermal radiation and dual stratification. The impact of binary chemical reaction with Arrhenius activation energy is also considered.

Modified fractional variational iteration method for solving the generalized time-space fractional Schrödinger equation.

Based on He's variational iteration method idea, we modified the fractional variational iteration method and applied it to construct some approximate solutions of the generalized time-space fractional Schrödinger equation (GFNLS). The fractional derivatives are described in the sense of Caputo. With the help of symbolic computation, some approximate solutions and their iterative structure of the GFNLS are investigated.

Homotopic approximate solutions for the perturbed CKdV equation with variable coefficients.

This work concerns how to find the double periodic form of approximate solutions of the perturbed combined KdV (CKdV) equation with variable coefficients by using the homotopic mapping method. The obtained solutions may degenerate into the approximate solutions of hyperbolic function form and the approximate solutions of trigonometric function form in the limit cases. Moreover, the first order approximate solutions and the second order approximate solutions of the variable coefficients CKdV equation in perturbation εu (n) are also induced.