Application of Variational Iteration Method to Nonlinear Differential Equations of Fractional Order

By Ζ.Μ. Odibat,, Shaher Momani. 2006

775 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d9c70d0ceb4e7925999c269a2e6eef972942bd59

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Citations in the corpus

Application of Variational Iteration Method to a General Riccati Equation (2007, methodology): “This method, which is a modified general Lagrange’s multiplier method [10], has been shown to solve effectively, easily and accurately a large class of nonlinear problems [11, 13, 15, 16, 12, 14, 23, 2, 20, 5].”
AN ALGORITHM FOR THE NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER (2008, methodology): “The application of the two methods is successfully extended to obtain an analytical approximate solutions to linear and nonlinear differential equations of fractional order [24-28,32,45-47].”
Solution of fractional-order differential equations based on the operational matrices of new fractional Bernstein functions (2017, methodology): “…and Momani, 2008), Taylor collocation method (Cenesiz et al., 2010), Jacobi operational matrix method (Kazem, 2013), Variational iteration method (Odibat and Momani, 2006), Legendre functions method (Kazem et al., 2013), Tau methods (Rad et al., 2014), A new operational matrix method…”
A generalized differential transform method for linear partial differential equations of fractional order (2008, methodology): “Several illustrative examples are given to demonstrate the effectiveness of the present method.”
Variational iteration method for fractional heat- and wave-like equations (2009, methodology): “From Momani and Odibat [6] [18] and also Shou and He [36], we study the multi-dimensional time fractional heat-and wave-like equations by using VIM.”
Properties of Caputo Operator and Its Applications to Linear Fractional Differential Equations (2015, methodology): “During the last decades, several methods have been proposed to solve fractional partial differential equations, fractional integro-differential equations and dynamic systems containing fractional derivatives, such as Adomian decomposition method [1, 2, 3 ], He’s variational iteration method [8], hom”
Variational iteration method: New development and applications (2007, methodology): “For example, Abbasbandy applied the variational iteration method to Riemann–Liouville’s fractional derivatives [10], Draganescu and his colleagues to nonlinear vibration with fractional damping [11], Momani and his colleagues applied the method to fluid mechanics where the fractional derivative was ”
He's homotopy perturbation method for solving systems of Volterra integral equations of the second kind (2009, neutral): “Introduction The Topic of the He’s homotopy perturbation method [1–6] has been rapidly growing in recent years [7–23].”
Bernoulli wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations (2014, methodology): “These methods include Fourier transforms [8], eigenvector expansion [9], Laplace transforms [10], Adomian decomposition method [11], variational iteration method [12], finite difference method (FDM) [13], the power series method [14], fractional differential transform method (FDTM) [15] and homotopy”