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The Daftardar-Gejji Jafari Method (DGJM) has been used extensively in the recent one and a half decades to solve various non-linear equations such as algebraic equations, integral equations, partial differential equations, ordinary and fractional differential equations and so on. In this paper, we present a new time-efficient algorithm for DGJM for solving non-linear fractional foam drainage and Zakharov-Kuznetsov equations. We compare the DGJM solutions with those obtained by the Adomian decomposition method and the homotopy perturbation method. The obtained results reveal that the new algorithm of DGJM is more effective and time-efficient for predicting the solutions to such problems that too without calculating tedious calculations such as finding Adomian's polynomials and constructing homotopy function.