Abstract

In this chapter, a reproducing kernel Hilbert space method (RKHSM) is proposed for studying time-fractional PDEs. Specifically, the RKHSM is applied for time-fractional heat-like and Navier-Stokes equations when the equations’ coefficients vary between constants and variables. These equations have significant applications in applied sciences and engineering. The current approach utilizes some important binary reproducing kernel Hilbert (RK) spaces with appropriate RK functions. Error estimations and convergence analysis of the proposed method are discussed. The RKHSM is assessed by testing some illustrative applications which have exact solutions. The results suggest that the RKHSM is a very effective and highly convenient method for solving time-fractional PDEs arising in widespread fields of engineering and applied sciences.