Solution of nonlinear fractional differential equations using homotopy analysis method

By M. Ganjiani. 2010

93 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/5a9739bcee3eeda192194457cd3e3e09bd4bc923

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In Biomedical Engineering

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

The homotopy analysis method for solving the time-fractional Fornberg-Whitham equation and comparison with Adomian's decomposition method (2013, methodology): “HAM has been successfully applied to solve many types of nonlinear problems in science and engineering by many others [24–28].”
Analytical solution of time-fractional two-component evolutionary system of order 2 by residual power series method (2015, methodology): “Such methods are: Variational iteration method and multivariate Pade approximations [21], Iterative Laplace transform method [13], Adomian decomposition method [12, 17–19, 22], Homotopy analysis method [10, 11], Laplace-Homotopy perturbation method [14], Decomposition method [15] and Sumudu transfor”
On convergence of homotopy analysis method and its application to fractional integro-differential equations (2013, methodology): “Some powerful methods have been applied to solve fractional differential equations, for example, differential transform method [8, 19] and homotopy analysis method [10, 15, 5, 13].”
Chebyshev operational matrix method for solving multi-order fractional ordinary differential equations (2013, methodology): “In this case, Adomian’s decomposition method [7, 8, 9, 10, 11, 12], homotopy perturbation method [13, 14], analytical homotopy method [15, 16, 17], differential transform method [18] are relatively”
Alternative variational iteration method for solving the time-fractional Fornberg–Whitham equation (2015, unknown): “, the finite difference method [11,12], reproducing kernel space method [13,14], Adams–Bashforth–Moulton method [15], homotopy perturbation method [16,17], Adomian decomposition method [18,19], homotopy analysis method [20,21], and generalized differential transform method [22,23].”
Computing Eigenelements of Sturm–Liouville Problems of Fractional Order via Fractional Differential Transform Method (2011, methodology): “These methods include the Adomian decomposition method (ADM) [6-8], variational iteration method (VIM) [9-11], homotopy perturbation method (HPM) [12-14], homotopy analysis method(HAM)[15-17] and other methods [18-20].”