Variational iteration method for the Burgers' flow with fractional derivatives -- new Lagrange multipliers

DOI10.1016/j.apm.2012.12.018zbMath1438.76046OpenAlexW2022422872MaRDI QIDQ1788729

Guo-Cheng Wu, Dumitru Baleanu

Publication date: 8 October 2018

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2012.12.018

zbMATH Keywords

Caputo derivativefractional differential equationvariational iteration method

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Flows in porous media; filtration; seepage (76S05) Variational methods applied to problems in fluid mechanics (76M30) Fractional derivatives and integrals (26A33) Numerical methods for initial value problems involving ordinary differential equations (65L05) Laplace transform (44A10) Fractional partial differential equations (35R11)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Variational iteration method for the time-fractional Fornberg-Whitham equation
• On the MHD flow of fractional generalized Burgers' fluid with modified Darcy's law
• Homotopy perturbation method for nonlinear partial differential equations of fractional order
• Application of numerical inverse Laplace transform algorithms in fractional calculus
• Variational iteration method and homotopy perturbation method for fourth-order fractional integro-differential equations
• Fractional relaxation-oscillation and fractional diffusion-wave phenomena.
• Variational iteration method -- a kind of non-linear analytical technique: Some examples
• Variational iteration method: New development and applications
• Numerical solutions of coupled Burgers equations with time- and space-fractional derivatives
• The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method
• An exact solution of start-up flow for the fractional generalized Burgers' fluid in a porous half-space
• Numerical algorithm based on Adomian decomposition for fractional differential equations
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• An approximation solution of a nonlinear equation with Riemann-Liouville's fractional derivatives by He's variational iteration method
• Variational iteration method for fractional heat- and wave-like equations
• On accelerated flows of a viscoelastic fluid with the fractional Burgers' model
• Numerical solution of the space fractional Fokker-Planck equation.
• Approximate analytical solution for seepage flow with fractional derivatives in porous media
• A predictor-corrector approach for the numerical solution of fractional differential equations
• Analytical approximate solutions for nonlinear fractional differential equations
• Multi-order fractional differential equations and their numerical solution
• Scaling limit solution of a fractional Burgers equation.
• Some helical flows of a Burgers fluid with fractional derivative
• Analytical approach to linear fractional partial differential equations arising in fluid mechanics
• Short memory principle and a predictor-corrector approach for fractional differential equations
• A second-order accurate numerical approximation for the fractional diffusion equation
• New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation