Analytical solution for the time fractional BBM-Burger equation by using modified residual power series method
type: Item
instance of: scholarly article
title: Analytical solution for the time fractional BBM-Burger equation by using modified residual power series method
zbMATH Open document ID: 1405.35190
DOI: 10.1155/2018/2891373
author: Jianke Zhang
author: Zhirou Wei
author: Yuelei Xiao
author: Longquan Yong
published in: Complexity
publication date: 2018-12-17T00:00:00Z
review text: Summary: In this study, a generalized Taylor series formula together with residual error function, which is named the residual power series method (RPSM), is used for finding the series solution of the time fractional Benjamin-Bona-Mahony-Burger (BBM-Burger) equation. The BBM-Burger equation is useful in describing approximately the unidirectional propagation of long waves in certain nonlinear dispersive systems. The numerical solution of the BBM-Burger equation is calculated by Maple. The numerical results show that the RPSM is reliable and powerful in solving the numerical solutions of the BBM-Burger equation compared with the exact solutions as well as the solutions obtained by homotopy analysis transform method through different graphical representations and tables.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 65M99
Mathematics Subject Classification ID: 35C10
zbMATH DE Number: 6994153
describes a project that uses: Maple
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/2891373
OpenAlex ID: W2894944938
cites work: Q5699297
cites work: Solution of fractional differential equations by using differential transform method
cites work: Basic theory of fractional differential equations
cites work: Multi-order fractional differential equations and their numerical solution
cites work: Application of variational iteration method to nonlinear differential equations of fractional order
cites work: On the homotopy analysis method for nonlinear problems.
cites work: An analytic algorithm for the space-time fractional advection-dispersion equation
cites work: The \((\frac{G'}{G})\)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
cites work: Analytic approximate solutions for a class of variable order fractional differential equations using the polynomial least squares method
cites work: An Explicit Finite Difference Method and a New von Neumann-Type Stability Analysis for Fractional Diffusion Equations
cites work: New results on fractional power series: theories and applications
cites work: Approximate analytical solution of the nonlinear fractional KdV-Burgers equation: a new iterative algorithm
cites work: A novel representation of the exact solution for differential algebraic equations system using residual power-series method
cites work: Q6104579
cites work: Approximate analytical solutions of time fractional Whitham-Broer-Kaup equations by a residual power series method
cites work: Construction of fractional power series solutions to fractional Boussinesq equations using residual power series method
cites work: Residual Power Series Method for Fractional Diffusion Equations
cites work: Residual power series method for solving time-space-fractional Benney-Lin equation arising in falling film problems
cites work: Analytical solution of the fractional Fredholm integrodifferential equation using the fractional residual power series method
cites work: Asymptotic solutions of time-space fractional coupled systems by residual power series method
cites work: A novel scheme for solving Caputo time-fractional nonlinear equations: theory and application
cites work: Analytical solution of the time-fractional Phi-4 equation by using modified residual power series method
cites work: Q2973303
cites work: ANALYTICAL SOLUTION OF TIME-FRACTIONAL TWO-COMPONENT EVOLUTIONARY SYSTEM OF ORDER 2 BY RESIDUAL POWER SERIES METHOD
cites work: The generalized BBM-Burgers equations: convergence results for conservation law with discontinuous flux function
cites work: Exact solutions of the time fractional BBM-Burgers equation by novel \((G^{\prime}/G)\)-expansion method
cites work: Approximate explicit solutions of nonlinear BBMB equations by homotopy analysis method and comparison with the exact solution
cites work: Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
Wikidata QID: Q129134916
description: scientific article; zbMATH DE number 6994153