Two novel computational techniques for fractional Gardner and Cahn-Hilliard equations

The numerical solutions for nonlinear fractional Gardner and Cahn-Hilliard equations arising in fluids flow are obtained with the aid of two novel techniques, namely, fractional natural decomposition method (FNDM) and q-homotopy analysis transform method (q-HATM). Both featured techniques are different from each other since FNDM is algorithmic by the aid of Adomian polynomial and q-HATM is defined by the help of homotopy polynomial. The numerical simulations have been conducted to verify that the proposed schemes are reliable and accurate. The outcomes are revealed through the plots and tables. The comparison of solution obtained by proposed schemeswith the available solutions exhibits that both the featured schemes are methodical, efficient, and very exact in solving the nonlinear complex phenomena.