This paper studies a simultaneous wireless information and power transfer (SWIPT)-aware fog computing network, where a multiple antenna fog function integrated hybrid access point (F-HAP) transfers information and energy to multiple heterogeneous single-antenna sensors and also helps some of them fulfill computing tasks. By jointly optimizing energy and information beamforming designs at the F-HAP, the bandwidth allocation and the computation offloading distribution, an optimization problem is formulated to minimize the required energy under communication and computation requirements, as well as energy harvesting constraints. Two optimal designs, i.e., fixed offloading time (FOT) and optimized offloading time (OOT) designs, are proposed. As both designs get involved in solving non-convex problems, there are no known solutions to them. Therefore, for the FOT design, the semidefinite relaxation (SDR) is adopted to solve it. It is theoretically proved that the rank-one constraints are always satisfied, so the global optimal solution is guaranteed. For the OOT design, since its non-convexity is hard to deal with, a penalty dual decomposition (PDD)-based algorithm is proposed, which is able to achieve a suboptimal solution. The computational complexity for two designs are analyzed. Numerical results show that the partial offloading mode is superior to binary benchmark modes. It is also shown that if the system is with strong enough computing capability, the OOT design is suggested to achieve lower required energy; Otherwise, the FOT design is preferred to achieve a relatively low computation complexity.