The flow of fluid with mas transfer is an important phenomenon in the industries and nature. A new scheme for formulating the Caputo time fractional model for the flow of Brinkman-type fluid between the plates was introduced using the generalized Fick's law. Within a channel, the free convection flow of the electrically conducted Brinkman-type fluid was considered. The governing equations were solved by the techniques of Fourier sine and the Laplace transform. In terms of the special function,

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... amely, the Mittag-Leffler function, final solutions were obtained. To explain the conceptual arguments of the embedded parameters, separate plots are represented in figures. It is worth noting that for increasing the values of the Brinkman-type fluid parameter, the velocity profile decreases.