Wright function solutions for mixed convection flow of micropolar fluid with memory effects: A Caputo fractional derivative approach

This investigation systematically examined mixed convection flow of a fractional micropolar fluid over an oscillating plate, incorporating thermal radiation and memory effects through Caputo fractional derivatives. The governing equations of the proposed problem were non-dimensionalized using appropriate dimensionless variables. Exact solutions for velocity, microrotation, and temperature distributions were derived via the Laplace transform method. The obtained exact solutions were expressed in terms of Wright functions to preserve memory characteristics. Special cases, including Stokes' first problem and fractional viscous fluids, were demonstrated, which showed the model's versatility. The influences of key parameters, such as fractional order ( $\alpha$), micropolar material parameter ( $\beta$), Grashof number ( $Gr$), Prandtl number ( $Pr$), and radiation parameter ( $R$) on flow and heat transfer characteristics, were analyzed and presented in various graphs. Graphical results illustrate parametric trends emphasizing memory effects, while tabulated data quantified skin friction, wall couple stress, and Nusselt number variations. The results yielded: (1) a generalized fractional micropolar model capturing memory effects, (2) new insights into radiation's role in thermal boundary layer modulation under non-local dynamics, and (3) benchmark solutions for microfluidic device design. This work unified fractional calculus (with its inherent memory effects), micropolar theory, and oscillatory boundary conditions, establishing a foundation for advanced fluid mechanics research.