Analytical approximate solutions for nonlinear fractional differential equations

By Nabil T. Shawagfeh. Applied Mathematics and Computation, 2002

295 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/dfaabe3fe7b0636c89ee234883f9a7a543f65dc5

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Spectral-Collocation Methods for Fractional Pantograph Delay-Integrodifferential Equations (2013, methodology): “Several analytical methods have been introduced to solve FDEs including various transformation techniques [6], operational calculus methods [7], the Adomian decomposition method [8], and the iterative and series-based methods [9].”
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].”
Analytical Solutions of the Space-Time Fractional Derivative of Advection Dispersion Equation (2013, methodology): “Some other analytical methods and their recent development for solving nonlinear fractional partial differential equation can found in the work done by [15–26] and the excellent book for analytical and numerical methods.”
Solving systems of fractional differential equations using differential transform method (2008, methodology): “Recently, theAdomian decomposition method and variational iteration method have been used for solving a wide range of problems [3,6,10–13,15–18,20].”
Solving a system of nonlinear fractional differential equations using Adomian decomposition (2006, methodology): “Shawagfeh [14] has employed Adomian decomposition in case of the nonlinear fractional differential equation: D y(x)=f (x, y), y(k)(0)=ck, 0 k [ ].”
Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution (2007, unknown): “In this way, a FPDE which received much attention in the literature is that one obtained by substituting fractional derivatives for the time derivative and the space derivative in the diusion equation [1,2,8,9,11,12,15, 35 ,36] and its generalizations.”
On the Finite Caputo and Finite Riesz Derivatives (2006, methodology): “We must mention that the ADM to solve the ordinary fractional differential equations has been used by several authors with good results (see, for example, [23, 25]).”
Adomian decomposition: a tool for solving a system of fractional differential equations (2005, methodology): “Shawagfeh [13] has employed this method for solving non-linear FDE.”
Variational iteration method for the Burgers' flow with fractional derivatives—New Lagrange multipliers (2013, unknown): “Some numerical methods [1–6] and analytical methods [7–12] have been developed for fractional differential equations (FDEs).”
A Tutorial Review on Fractal Spacetime and Fractional Calculus (2014, unknown): “There are various analytical methods for fractional calculus, among which the variational iteration method [28, 50, 56, 69–75], the homotopy perturbation method [57, 76–92], the fractional complex transform [93–96], Yang-Laplace transform [44–46], and Yang-Fourier transform [44–46] have received muc”