This study aims to numerically investigate the Marangoni convective flow of nanoliquid initiated by surface tension and heading towards a radiative Riga surface. The surface tension appears in the problem due to the gradients of temperature and concentration at the interface. The influence of first order chemical reaction is involved in the system with sufficient boundary conditions. Set of governing nonlinear PDEs is transformed into highly nonlinear ODEs using suitable transformations. HAM is applied for convergent series solutions. Impact of various pertinent fluid parameters on momentum, thermal and solutal boundary layers is analyzed graphically. The chemical reaction plays vital role in saturation of nanoparticles in the base fluid near the surface as well as away from it. The Lorentz forces originated by the Riga surface become powerful when the radiation parameter comes into effect. The significance of Riga plate is thus more prominent through thermal radiation. However, the magnetic effect dampens down for higher radiation parameter. Fluid parameters, Nusslt and Sherwood numbers are analyzed with detailed discussion and concluding remarks.

The main purpose of this article is to obtain the new solutions of fractional bad and good modified Boussinesq equations with the aid of auxiliary equation method, which can be considered as a model of shallow water waves. By using the conformable wave transform and chain rule, nonlinear fractional partial differential equations are converted into nonlinear ordinary differential equations. This is an important impact because both Caputo definition and Riemann–Liouville definition do not satisfy the chain rule. By using conformable fractional derivatives, reliable solutions can be achieved for conformable fractional partial differential equations.

This paper proposes obtaining the new wave solutions of time fractional sixth order nonlinear Equation (KdV6) using sub-equation method where the fractional derivatives are considered in conformable sense. Conformable derivative is an understandable and applicable type of fractional derivative that satisfies almost all the basic properties of Newtonian classical derivative such as Leibniz rule, chain rule and etc. Also conformable derivative has some superiority over other popular fractional derivatives such as Caputo and Riemann-Liouville. In this paper all the computations are carried out by computer software called Mathematica.

Present article aims to investigate the heat and mass transfer developments in boundary layer Jeffery nanofluid flow via Darcy-Forchheimer relation over a stretching surface. A viscous Jeffery naonfluid saturates the porous medium under Darcy-Forchheimer relation. A variable magnetic effect normal to the flow direction is applied to reinforce the electro-magnetic conductivity of the nanofluid. However, small magnetic Reynolds is considered to dismiss the induced magnetic influence. The so-formulated set of governing equations is converted into set of nonlinear ODEs using transformations. Homotopy approach is implemented for convergent relations of velocity field, temperature distribution and the concentration of nanoparticles. Impact of assorted fluid parameters such as local inertial force, Porosity factor, Lewis and Prandtl factors, Brownian diffusion and Thermophoresis on the flow profiles is analyzed diagrammatically. The drag force (skin-friction) and heat-mass flux is especially analyzed through numerical information compiled in tabular form. It has been noticed that the inertial force and porosity factor result in decline of momentum boundary layer but, the scenario is opposite for thermal profile and solute boundary layer. The concentration of nanoparticles increases with increased porosity and inertial effect however, a significant reduction is detected in mass flux.

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In this paper, an alternative method has been studied for traveling wave solutions of mathematical models which have an important place in applied sciences and balance term is not integer. With this method, the trigonometric, hyperbolic, complex and rational type traveling wave solutions of the (1[Formula: see text]+[Formula: see text]1)-dimensional resonant nonlinear Schrödinger’s (RNLS) equation with the parabolic law have constructed. This method can be applied reliably and effectively in many differential equations.

This manuscript focuses on the application of the (m+1/G′)-expansion method to the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation. With the help of projected method, the periodic and singular complex wave solutions to the considered model are derived. Various figures such as 3D and 2D surfaces with the selecting the suitable of parameter values are plotted.

In this paper, a new solution process of ( 1 / G ′ ) -expansion and ( G ′ / G , 1 / G ) -expansion methods has been proposed for the analytic solution of the Zhiber-Shabat (Z-S) equation. Rather than the classical ( G ′ / G , 1 / G ) -expansion method, a solution function in different formats has been produced with the help of the proposed process. New complex rational, hyperbolic, rational and trigonometric types solutions of the Z-S equation have been constructed. By giving arbitrary values to the constants in the obtained solutions, it can help to add physical meaning to the traveling wave solutions, whereas traveling wave has an important place in applied sciences and illuminates many physical phenomena. 3D, 2D and contour graphs are displayed to show the stationary wave or the state of the wave at any moment with the values given to these constants. Conditions that guarantee the existence of traveling wave solutions are given. Comparison of ( G ′ / G , 1 / G ) -expansion method and ( 1 / G ′ ) -expansion method, which are important instruments in the analytical solution, has been made. In addition, the advantages and disadvantages of these two methods have been discussed. These methods are reliable and efficient methods to obtain analytic solutions of nonlinear evolution equations (NLEEs).