Application of homotopy analysis method to fractional KdV–Burgers–Kuramoto equation

By Lina Song, Hong-qing Zhang. 2007

208 citations recorded by the source corpus.

Subfields: Geometry and Topology, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/723eb24c700a5aabf1b4ba5716217bef2371dbba

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Citations in the corpus

An adaptation of homotopy analysis method for reliable treatment of strongly nonlinear problems: construction of homotopy polynomials (2015, methodology): “For more details about the applications of the method, the reader is advised to consult the research works presented in [7–36] or the references therein.”
Notes on the homotopy analysis method: Some definitions and theorems (2009, background): “In most cases, the zeroth-order deformation equation (16) can give satisfied homotopyseries solution, if the auxiliary linear operator L, the auxiliary function Hð~x; tÞ and convergence-control parameter h are properly chosen, as pointed out by Liao [21–23,25,60,26] and others [28–59].”
Approximate Analytical Solution to Time-Fractional Damped Burger and Cahn-Allen Equations (2013, methodology): “This method has been successfully applied for solving several nonlinear problems arising in science and engineering by many authors [1–16] and the references therein.”
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].”
Solving nonlinear fractional partial differential equations using the homotopy analysis method (2010, methodology): “Similar to integer-order differentiation, Caputo’s fractional differentiation is a linear operation [33, 64] D(λf (t) + μg(t)) = λDf (t) + μDg(t), (2.”
Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation (2009, unknown): “This fact has been pointed out by many researchers, such as Abbasbandy [2], Liao et al [12], Bataineh et al [14], Van Gorder et al [15], Hayat and Sajid [16][17], and Song et al [18].”