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In this work, an efficient numerical approximation for the solution of the time fractional nonlinear diffuse interface model is studied. The solution to this problem has a weak singularity near the initial time t = 0. The fractional order nonlinear diffusion model is transformed into a system of nonlinear functional equations. The Daftardar-Gejji and Jafari method is employed to solve the corresponding nonlinear system. The L1 scheme is used to discretize the Caputo fractional derivative on a graded mesh in the time direction. In contrast, the spatial derivative is approximated by applying a classical central finite difference scheme to a uniform mesh. The convergence analysis and the error bounds are carried out. The analysis and the computational findings exhibit the effectiveness of the proposed method.

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