Construction of Fractional Power Series Solutions to Fractional Boussinesq Equations Using Residual Power Series Method

By Fei Xu, Yixian Gao, Xuehua Yang, Heng Zhang. 2016

58 citations recorded by the source corpus.

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 . Using RPSM, we can obtain FPS solutions of fourth-, sixth-, and 2th-order time-space fractional Boussinesq equations in and fourth-order time-space fractional Boussinesq equations in and . 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.

Subfields: Geometry and Topology, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/763dfc1745491f80a3ec553fdc85a01a434ef9ff

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Citations in the corpus

• Iterative methods for solving fourth‐ and sixth‐order time‐fractional Cahn‐Hillard equation (2019, background): “Thus, Equation (47) gives an approximate solution to problem (42) in terms of convergence parameter h and n.”