Construction of fractional power series solutions to fractional Boussinesq equations using residual power series method
type: Item
instance of: scholarly article
title: Construction of fractional power series solutions to fractional Boussinesq equations using residual power series method
zbMATH Open document ID: 1400.35227
DOI: 10.1155/2016/5492535
author: Yanyan Li
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35C10
zbMATH DE Number: 6953330
Wikidata QID: Q59131609
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/5492535
OpenAlex ID: W2394601494
cites work: Approximate analytical solution for seepage flow with fractional derivatives in porous media
cites work: Approximate analytical solution of the nonlinear fractional KdV-Burgers equation: a new iterative algorithm
cites work: New results on fractional power series: theories and applications
cites work: Variational Methods for Nonlocal Fractional Problems
cites work: Q3408155
cites work: Q3141902
cites work: The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
cites work: Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
cites work: Q3141895
cites work: A reliable analytical method for solving higher-order initial value problems
cites work: Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations
cites work: Global existence and decay of solutions for the generalized bad Boussinesq equation
cites work: Advances in Fractional Calculus
cites work: Q5693987
cites work: Modified variational iteration method for Boussinesq equation
cites work: Construction of analytic solution for time-fractional Boussinesq equation using iterative method
cites work: Fractional Lie group method of the time-fractional Boussinesq equation
cites work: Definition of Physically Consistent Damping Laws with Fractional Derivatives
cites work: Q5699297
cites work: Fractional derivatives for physicists and engineers. Volume I: Background and theory. Volume II: Applications
description: scientific article; zbMATH DE number 6953330