Analytical solution of the time-fractional Phi-4 equation by using modified residual power series method

Iterative methods for solving fourth‐ and sixth‐order time‐fractional Cahn‐Hillard equation

“…Solving partial differential equations with fractional derivatives is often more difficult than solving the classical type, for its operator is defined by integral. In the recent year, researchers have developed some iterative methods for solving the nonlinear fractional differential equations, such as Adomian decomposition method, variational iteration method, homotopy decomposition method, differential transform method, permuturbation iteration transformation method, homotopy‐perturbation method, homotopy analysis method, exp‐function method, wavelet method, Khater method, and residual power series method …”

“…In the recent year, researchers have developed some iterative methods for solving the nonlinear fractional differential equations, such as Adomian decomposition method, 21,28,29 variational iteration method, [30][31][32] homotopy decomposition method, 33 differential transform method, 34,35 permuturbation iteration transformation method, 36 homotopy-perturbation method, 28,37 homotopy analysis method, [38][39][40] exp-function method, [41][42][43] wavelet method, 44 Khater method, 45 and residual power series method. 46,47 In this paper, we consider the time-fractional Cahn-Hilliard (TFCH) equations of the fourth and sixth order given, respectively, as follows:…”

Revisited Fisher’s equation in a new outlook: A fractional derivative approach

“…Applications, concluding remarks and some theory with regard to the RPS method can be found in Refs. [23,21,22,[24][25][26][27].…”

Analytic solution of homogeneous time-invariant fractional IVP

“…Almost all attempts were developed by either finding nu-merical solutions over a specific range or considering few terms of an iterative computational series solution as an approximate. Such available methods are (He's) variational iteration methods [11,12], the iterative Laplace transform method [13], Adomian's decomposition method [14], the differential transform method [15,16], homotopy analysis/perturbation methods [17,18], the homotopy analysis-Laplace transform method [19], Chebyshev/Jacobi/Legendre operational matrix methods [20], the fractional Lie group method [21], the generalized Taylor power series method [22,23], and the residual power series method [24][25][26][27][28].…”