Formable transform Adomian decomposition method for solving nonlinear time-fractional diffusion equation

Nonlinear time-fractional diffusion equations (NTFDEs) are widely applied for modeling various natural processes like volcanic eruption, diffusion processes, earthquakes, brain tumors, and the dynamics of soil in water. Solving these problems is quite challenging. So, designing effective numerical approaches is an active research area. The fractional derivative used is the Caputo type. In this paper, we develop the hybrid series based method by combining the Formable transform and Adomian decomposition method (ADM) for treating the NTFDEs. The stability and convergence of the developed series based method have been investigated. The effectiveness of the introduced method is investigated by solving two test examples. The obtained numerical results show that the proposed method is efficient for solving NTFDEs and gives accurate results.