HOMOTOPY ANALYSIS METHOD FOR FRACTIONAL IVPS

By Ishak Hashim, O. Abdulaziz, Shaher Momani. 2009

475 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/483bd4ca3917048ab358b811a81932c87959faa2

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

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”
THE CONSTRUCTION OF OPERATIONAL MATRIX OF FRACTIONAL DERIVATIVES USING B-SPLINE FUNCTIONS (2012, methodology): “There are several techniques for solving such equations like Adomian decomposition method [14,27,30,35,43], He’s variational iteration method [17,29,31], homotopy perturbation method [29,40], homotopy analysis method [16], collocation method [34], Galerkin method [12] and other methods [21,24].”
A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations (2011, methodology): “There are some further methods, such as operational method [9], homotopy analysis method [10], differential transform method [11–13] and other methods [6,14–18].”
The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative (2014, methodology): “There are analytical methods and numerical methods for solving the differential equations, such as the finite element method [6], the harmonic wavelet method [7–9], the Adomian decomposition method [10–12], the homotopy analysismethod [13, 14], the homotopy decomposition method [15, 16], the heat ba”
A new operational matrix for solving fractional-order differential equations (2010, methodology): “Consider the following linear initial value problem [29,32] Dy(x)+ y(x) = 0, 0 < α < 2, y(0) = 1, y(0) = 0.”
Numerical solution of fractional differential equations with a Tau method based on Legendre and Bernstein polynomials (2014, methodology): “Example 2 In this example, we consider the following linear initial value problem, [21, 23] Dy.”
On the numerical solutions for the fractional diffusion equation (2011, methodology): “Recently, several numerical methods to solve the fractional differential equations have been given such as variational iteration method [6], homotopy perturbation method [15], Adomian’s decomposition method [7], homotopy analysis method [4] and collocation method [12].”
GEGENBAUER WAVELETS OPERATIONAL MATRIX METHOD FOR FRACTIONAL DIFFERENTIAL EQUATIONS (2015, methodology): “Some of these techniques include, fractional difference method [25], differential transform method [2], Adomian decomposition method [14] and homotopy analysis method [16].”