Construction of fractional power series solutions to fractional Boussinesq equations using residual power series method (Q1793310)

Summary: This paper is aimed at constructing fractional power series (FPS) solutions of time-space fractional Boussinesq equations using residual power series method (RPSM). Firstly we generalize the idea of RPSM to solve any-order time-space fractional differential equations in high-dimensional space with initial value problems in \(\mathbb{R}^n\). Using RPSM, we can obtain FPS solutions of fourth-, sixth-, and 2\(n\)th-order time-space fractional Boussinesq equations in \(\mathbb{R}\) and fourth-order time-space fractional Boussinesq equations in \(\mathbb{R}^2\) and \(\mathbb{R}^n\). Finally, by numerical experiments, it is shown that RPSM is a simple, effective, and powerful method for seeking approximate analytic solutions of fractional differential equations.