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Abstract

The research delves into the intricate study of the fractional model of unsteady and incompressible MHD Brinkman fluid between vertical plates. Various fractional derivatives, along with appropriate boundary conditions, such as Caputo, Caputo-Fabrizio, Antangna Baleanu, and Prabhakar are applied. The non-dimensional equations are skillfully tackled using the Laplace transform method. The resulting solution for energy and momentum is presented in a series form. The study also delves into the intriguing influence of memory parameters on the temperature and velocity field, visually representing the mathematical outcomes for temperature and velocity fields across different parameters. Furthermore, the study provides insightful comparisons between different fractional derivatives, shedding light on their respective impacts on the temperature and velocity fields.