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In this paper, we present a class of numerical schemes and apply it to the diffusion equations. The objective is to obtain numerical solutions of the constructive equations of a type of Casson fluid model. We investigate the solutions of the free convection flow of the Casson fluid along with heat and mass transfer in the context of modeling with the fractional operators. The numerical scheme presented in this paper is called the fractional version of the Adams Basford numerical procedure. The advantage of this numerical technique is that it combines the Laplace transforms and the classical Adams Basford numerical procedure. Note that the usage of the Laplace transforms makes possible the applicability of the numerical approach to diffusion equations in general. The Caputo derivative will be used in the investigations. The influence of the considered Casson fluid model parameters as the Prandtl number  Pr , the Schmidt number  Sc , the material parameter of the Casson fluid  β , and the order of the Caputo fractional derivative on the dynamics of the temperature, concentration, and velocity profiles has been presented analyzed. Graphical representations have supported the results of the paper.

A Numerical Algorithm Applied to Free Convection Flows of the Casson Fluid along with Heat and Mass Transfer Described by the Caputo Derivative