On the stability of iteration methods for special solution of time-fractional generalized nonlinear ZK-BBM equation

An investigation of a possible description of non-linear wave was performed inside the scope of fractional order derivative. A clear motivation underpinning the extension of this study within the concept of fractional calculus was presented. The special solution of the extended equation was derived using an efficient iteration method called homotopy decomposition method. A theorem underpinning the uniqueness of the special solution was proposed and proved in detail. An investigation for stability of the iteration method for solving the extended equation was presented in detail. Numerical simulations were carried out using the proposed algorithm for different values of alpha and n.