In this article, we consider the effects of double diffusion on magnetohydrodynamics (MHD) Carreau fluid flow through a porous medium along a stretching sheet. Variable thermal conductivity and suction/injection parameter effects are also taken into the consideration. Similarity transformations are utilized to transform the equations governing the Carreau fluid flow model to dimensionless non-linear ordinary differential equations. Maple software is utilized for the numerical solution. These solutions are then presented through graphs. The velocity, concentration, temperature profile, skin friction coefficient, and the Nusselt and Sherwood numbers under the impact of different parameters are studied. The fluid flow is analyzed for both suction and injection cases. From the analysis carried out, it is observed that the velocity profile reduces by increasing the porosity parameter while it enhances both the temperature and concentration profile. The temperature field enhances with increasing the variable thermal conductivity and the Nusselt number exhibits opposite behavior.

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This article examined the effects of boundary layer flow and heat transport of a two-dimensional incompressible magnetohydrodynamic tangent hyperbolic fluid under slip boundary conditions and variable thermal conductivity. The entropy generation model is also analysed for the said fluid. Non-similarity transformations transformed the governing equations of the fluid and entropy generation model into dimensionless form. Maple software is used to solve the transformed equations numerically. Effects of different dimensionless parameters on entropy generation rate, Bejan number, velocity and temperature fields are studied thoroughly through graphs. It is observed that for higher values of velocity slip parameter and power-law index, the entropy generation rate decreases while the Bejan number increases. Also, for the Hartmann number, Weissenberg number and Brinkman number, we found an increase in the entropy generation rate, and reverse behaviour is observed for the Bejan number. Nusselt number, temperature profile and Bejan’s number increase with an increase in variable thermal conductivity.

We analytically investigate a nonlinear fractional-order sine-Gordon (sG) equation. The derivatives considered herein, are taken in Caputo’s sense. The Laplace transform together with the Adomian decomposition method (LADM) is applied to attain analytical approximation of the aforesaid equation. The sG equation having Caputo derivative is solved in the order of series solutions and the results are confirmed by considering two examples with appropriate initial conditions. The numerical simulations are accomplished to compare with the analytical approximations, where qualitatively better agreements are achieved.

This paper deals with the existence of solutions for a class of fractional order differential equations having m -points boundary conditions involving the Caputo fractional derivative. Moreover the nonlinearity also depend on the Caputo fractional derivative. We obtain sufficient conditions for the existence and uniqueness of solutions via Schauder's fixed-point theorem and Banach contraction principle. We provide an example to illustrate the applicability of our results. (2010): 26A33, 34A37, 34B05. Mathematics subject classification