This article provides numerical simulations of the time-fractional coupled Korteweg–de Vries and Klein–Gordon equations via the local meshless collocation method (LMCM) utilising the radial basis functions. The recommended local meshless technique is utilised for the space derivatives of the models whereas Caputo fractional definition is used for time-fractional derivative. Numerical experiments are performed for one-dimensional coupled Korteweg–de Vries and two-dimensional Klein–Gordon equations. In order to verify the efficiency and accuracy of the proposed meshless method, numerical results are compared with exact and numerical techniques reported in recent literature which reveals that the method is computationally attractive and produces better results.

Non-Newtonian materials have attracted the attention of scientists and engineers due to their many applications in the current era. This endeavour is conducted to utilise the generalised Ohm law with thermal and mass transportation. Phenomena of heat and mass transfer are based on generalised Fourier and Fick’s laws respectively. Present analysis examines magnetohydrodynamic (MHD) three-dimensional flow of the Casson liquid.Flow is assumed to be over a stretched surface which is stretched in two directions. Contribution of Hall and ion slip effects are included. Diffusion phenomenon is captured using the Boungrino model. Convergent series solutions by homotopy algorithm is also derived. Physical quantities of interest are discussed with respect to the involved variables. Convergence of the applied scheme is presented in the form of error analysis. Also convergence is shownby computing dimensionless stresses, heat and mass transfer rates. Authenticity of the achieved result is shown by comparing the obtained results with those from the open literature and excellent similarity is attained and recorded.Diffusion of mass and heat can be controlled by enhancing the thermal, solutal factors and Prandtl and Schmidt numbers.