Unveiling memory-driven dynamics: Fractional calculus and microswimmer trajectories in 1D shear flow

This study investigates the captivating dynamics of spherical microswimmers in a 1D shear flow, revealing the intricate interplay between memory effects and fluid mechanics through the lens of fractional calculus. By deriving exact solutions for the orientation and trajectory of these microswimmers, we uncover a rich tapestry of motion patterns that challenge traditional models. Our findings not only enhance the theoretical understanding of microswimmer behavior but also hold significant implications for practical applications in biophysics and targeted drug delivery. This research underscores the power of fractional calculus as a transformative tool in unraveling the complexities of biological systems, paving the way for innovative approaches in the study of fluid dynamics.