Fractional sub-equation method and its applications to nonlinear fractional PDEs

By Sheng Zhang, Hong-qing Zhang. 2011

528 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d7344bce731426b2766e7f4d1904af88ca8e6ab0

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Citations in the corpus

Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations (2013, methodology): “In recent decades, some effective methods for fractional calculus appeared in open literature, such as the exp-function method [5], the fractional subequation method [6–8], the (G/G)-expansion method [9, 10], and the first integral method [11].”
Local fractional series expansion method for solving wave and diffusion equations on Cantor sets (2013, methodology): “Various methods, for example, the Adomian decomposition method [10], the Rach-Adomian-Meyers modified decompositionmethod [11], the variational iteration method [12, 13], the homotopy perturbation method [13, 14], the fractal Laplace and Fourier transforms [15], the homotopy analysismethod [16], the”
New exact solutions of Burgers’ type equations with conformable derivative (2017, background): “[19] In recent years, scientists applied many approaches to solve nonlinear PDEs such as homotopy analysis method [20], sub-equation method [21], homotopy perturbation method [22], exponential rational function method [23], first integral method (FIM) [24,25], etc.”
Exact solutions for nonlinear partial fractional differential equations (2012, methodology): “Recently Zhang etal [12] have introduced a direct method called the subequation method to look for the exact solutions for nonlinear partial fractional differential equations.”
Exact solutions of nonlinear time fractional partial differential equations by sub‐equation method (2015, methodology): “In recent years, many powerful and efficient methods have been proposed to obtain exact solutions of partial differential equations, such as the fractional sub-equation method [6–9], the (G’/G)-expansion method [10, 11], the exp-function method [12, 13], the first integral method [14], the functiona”