In this chapter, we selectively present global methods for efficiently solving FPDEs, employing the basis functions introduced in Chapters 2 and 3. Here, we adopt the term global often in the context of space-time, considering time as another (space-like) spectral direction. We examine a number of typical FPDEs, which we introduced and probabilistically interpreted in Chapter 1, including: the subdiffusion equation, tempered fractional diffusion on the half/whole line, in addition to the generalized and unified (1+d)-dimensional sub-to-superdiffusion FPDE model for d≥1, where a single FPDE form can model a range of physical processes by just varying the corresponding temporal/spatial fractional derivatives in the model, hence, rendering the FPDE elliptic, parabolic, and/or hyperbolic on the (1+d)-dimensional space-time hypercube. In this chapter, we employ one-sided, two-sided, constant/variable-order, and fully distributed order fractional operators, introduced in Chapters 1 and 2.