Fractional partial differential equations are useful tools to describe transportation, anomalous, and non-Brownian diffusion. In the present paper, we propose the Daftardar-Gejji and Jafari method along with its error analysis for solving systems of nonlinear time–space fractional partial differential equations (PDEs). Moreover, we solve a variety of nontrivial time–space fractional systems of PDEs. The obtained solutions either occur in exact form or in the form of a series, which converges to a closed form. The proposed method is free from linearization and discretization and does not include any tedious calculations. Moreover, it is easily employable using the computer algebra system such as Mathematica, Maple, etc.