Mobile edge computing (MEC) is a promising paradigm for real-time applications with intensive computational needs (e.g., autonomous driving), as it can reduce the processing delay. In this work, we focus on the timeliness of computational-intensive updates, measured by Age-of-Information (AoI), and study how to jointly optimize the task updating and offloading policies for AoI with fractional form. Specifically, we consider edge load dynamics and formulate a task scheduling problem to minimize the expected time-average AoI. The uncertain edge load dynamics, the nature of the fractional objective, and hybrid continuous-discrete action space (due to the joint optimization) make this problem challenging and existing approaches not directly applicable. To this end, we propose a fractional reinforcement learning (RL) framework and prove its convergence. We further design a model-free fractional deep RL (DRL) algorithm, where each device makes scheduling decisions with the hybrid action space without knowing the system dynamics and decisions of other devices. Experimental results show that our proposed algorithms reduce the average AoI by up to compared with several non-fractional benchmarks.