Abstract. Continuous time random walks, which generalize random walks by adding a stochastic time between jumps, provide a useful description of stochastic transport at mesoscopic scales. The continuous time random walk model can accommodate certain features, such as trapping, which are not manifest in the standard macroscopic diffusion equation. The trapping is incorporated through a waiting time density, and a fractional diffusion equation results from a power law waiting time. A generalized continuous time random walk model with biased jumps has been used to consider transport that is also subject to an external force. Here we have derived the master equations for continuous time random walks with space-and time-dependent forcing for two cases: when the force is evaluated at the start of the waiting time and at the end of the waiting time. The differences persist in low order spatial continuum approximations; however, the two processes are shown to be governed by the same Fokker-Planck equations in the diffusion limit. Thus the fractional FokkerPlanck equation with space-and time-dependent forcing is robust to these changes in the underlying stochastic process. 1. Introduction. A continuous time random walk (CTRW) is a stochastic process where a particle arrives at a position, waits for a stochastic time, and stochastically jumps to a new position. The motion of the particle is governed by waiting time, and step length, probability densities [40]. Generalized CTRWs have been used as a stochastic basis for deriving fractional diffusion equations [16,22,36], fractional Cattenao equations [12], fractional reaction diffusion equations [53,20,39,14,52,3,49], fractional cable equations [21,27,28], fractional Fokker-Planck equations (FFPEs) [35,46,8,3], and fractional chemotaxis equations [26,15]. The evolution equation for the probability density function (PDF) of the random walking particles in a CTRW can be written as generalized master equations (GMEs) [45,24]. If the waiting times are exponentially distributed and the step length density is Gaussian, then in the diffusion limit the evolution equation for the PDF of the random walking particles is the standard diffusion equation. The CTRW also allows for anomalous diffusion in which the mean squared displacement increases slower (subdiffusion) or faster (superdiffusion) than linearly with time. The canonical case is a fractional power of time x 2 (t) ∼ t γ where γ = 1 [36]. Subdiffusion (0 < γ < 1) arises from CTRWs with power law waiting time densities such as Pareto or Mittag-Leffler waiting time densities. In this case, in the diffusion limit the evolution equation for the particle