Maxey–Riley equation: newer perspective

Non-integer-order derivatives have proven useful while modelling natural systems involving memory effects. In this article, we analyse the Maxey–Riley (M–R) equation that models the motion of a small particle in a non-uniform flow field. Fractional derivative arises naturally as a history term. We study the M–R equation in terms of fractional differential equations, a subject very well studied in recent times. This approach helps in gaining a deeper understanding of the underlying phenomenon. We observe solution curves having self-intersections, which is a novel feature of fractional-order dynamics.