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.

In this paper, the solution methodology of higher-order linear fractional partial deferential equations (FPDEs) as mentioned in eqs (1) and (2) below in Caputo definition relies on a new analytical method which is called the Laplace-residual power series method (L-RPSM). The main idea of our proposed technique is to convert the original FPDE in Laplace space, and then apply the residual power series method (RPSM) by using the concept of limit to obtain the solution. Some interesting and important numerical test applications are given and discussed to illustrate the procedure of our method, and also to confirm that this method is simple, understandable and very fast for obtaining the exact and approximate solutions (ASs) of FPDEs compared with other methods such as RPSM,variational iteration method (VIM), homotopy perturbation method (HPM) and Adomian decomposition method (ADM). The main advantage of the proposed method is its simplicity in computing the coefficients of terms of series solution by using only the concept of limit at infinity and not as the other well-known analytical method such as, RPSM that need to obtain the fractional derivative (FD) each time to determine the unknown coefficients in series solutions, and VIM, ADM, or HPM that need the integration operators which is difficult in fractional case.