A new algorithm for calculating Adomian polynomials for nonlinear operators
Applied Mathematics and Computation
Variational iteration method for autonomous ordinary differential systems
Applied Mathematics and Computation
An explicit and numerical solutions of the fractional KdV equation
Mathematics and Computers in Simulation
Variational iteration method-Some recent results and new interpretations
Journal of Computational and Applied Mathematics
Numerical approach to differential equations of fractional order
Journal of Computational and Applied Mathematics
Variational iteration method: New development and applications
Computers & Mathematics with Applications
The variational iteration method for solving linear and nonlinear systems of PDEs
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Comparison between Adomian's method and He's homotopy perturbation method
Computers & Mathematics with Applications
Reliable approaches of variational iteration method for nonlinear operators
Mathematical and Computer Modelling: An International Journal
Decomposition methods: A new proof of convergence
Mathematical and Computer Modelling: An International Journal
He's variational iteration method for treating nonlinear singular boundary value problems
Computers & Mathematics with Applications
The non-standard finite difference scheme for linear fractional PDEs in fluid mechanics
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Computers & Mathematics with Applications
A study on the convergence of variational iteration method
Mathematical and Computer Modelling: An International Journal
Computers & Mathematics with Applications
The fractional-order modeling and synchronization of electrically coupled neuron systems
Computers & Mathematics with Applications
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Variational iteration method has been used to handle linear and nonlinear differential equations. The main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently. In this work, a general framework of the variational iteration method is presented for analytical treatment of fractional partial differential equations in fluid mechanics. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include the fractional wave equation, fractional Burgers equation, fractional KdV equation, fractional Klein-Gordon equation and fractional Boussinesq-like equation are investigated to show the pertinent features of the technique. Comparison of the results obtained by the variational iteration method with those obtained by Adomian decomposition method reveals that the first method is very effective and convenient. The basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus.