Computational Fractional Dynamical Systems
by Rajarama M. Jena, Subrat K. Jena, Snehashish Chakraverty
20The Modified Simple Equation Method
20.1 Introduction
In the last few years, the modified simple equation (MSE) method, which is an analytical method, has become very popular. This approach is robust because it uses a general solution form defined by the finite series sum containing the unknown function. The characteristic of the technique enables the derivation of new and more general solitary wave solutions by substituting particular values for arbitrary coefficients in the exact solutions. The methods, such as the modified extended Tanh function method, the sine‐cosine method, the generalized Kudryashov method, the improved F‐expansion method, etc., work on the principle of certain particular preset functions or a solution to the auxiliary equation. These approaches require lengthy computation to solve the system of algebraic equations. However, in the MSE method, any preset function is not predefined, or a solution of any predetermined equation is not considered. As a result, this strategy may yield some novel solutions. The MSE method is recently being used to obtain exact solutions to a variety of fractional partial differential equations, including the space–time fractional modified regularized long‐wave equation, the space–time fractional modified Korteweg‐de Vries equation, the space–time fractional coupled Burgers’ equations (Kaplan et al. 2015), the nonlinear time‐fractional Sharma‐Tasso‐Oliver equation (Zayed et al. 2016), the generalized fractional reaction Duffing ...