  Transport equations with a nonlocal velocity field have been introduced as a
continuum model for interacting particle systems arising in physics, chemistry
and biology. Fractional time derivatives, given by convolution integrals of the
time-derivative with power-law kernels, are typical for memory effects in
complex systems. In this paper we consider a nonlinear transport equation with
a fractional time-derivative. We provide a well-posedness theory for weak
measure solutions of the problem and an integral formula which generalizes the
classical push-forward representation formula to this setting.
