Solving System of Fractional Differential Equations by Fractional Complex Transform Method

Optimal Homotopy Anaylsis Method for Nonlinear Partial Fractional Differential Fisher's Equation

“…(22) at = = 1 takes the form u x t = 1 1 + e x−5t 2 (23) and we have suggest the initial condition to Eq. (22) as following The fractional complex transformation (20) and (21) converting the nonlinear time space fractional Eq.…”

A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations

“…In recent years, many analytical and numerical methods have been used to solve linear and nonlinear fractional differential equations such as Adomian Decomposition Method [7][8][9][10], Homotopy Analysis Method [11], Laplace Decomposition Method [12], Homotopy Perturbation Method [13,14], and Yang Laplace transform [15]. Moreover, local fractional variational iteration method [16,17], Cylindrical-Coordinate method [18], modified Laplace Decomposition Method [12,19], and fractional complex transform method [20] are also applied to linear and nonlinear fractional partial differential equations. The asymptotic behavior of solutions of a weighted Cauchy-type nonlinear fractional partial differential equations is studied in [21][22][23].…”

Variational homotopy perturbation method for solving the generalized time-space fractional Schrdinger equation

“…To find explicit solutions of linear and nonlinear fractional differential equations, many powerful methods have been used such as the homotopy perturbation method (Momani and Odibat, 2007;Wang, 2008;Gupta and Singh, 2011), the Adomain decomposition method (Ray, 2009;Herzallah and Gepreel, 2012;Rida et al, 2008), the variational iteration method (He, 2000(He, , 2004(He, , 2007He and Wang, 2007), the homotopy analysis method (Hemida et al, 2012;Gepreel and Mohamed, 2013;Ganjiani, 2010;Behzadi, 2011), the fractional complex transform (Ghazanfari, 2012;Su et al, 2013), the homotopy perturbation Sumudu transform method (Karbalaie et al, 2014;Mahdy et al, 2015), the local fractional variation iteration method He and Liu, 2013;Yang et al, 2014), the local fractional Adomain decomposition method (Yang et al, 2013b), the Cantor-type Cylindrical-Coordinate method (Yang et al, 2013c), the variational iteration method with Yang-Laplace , the Yang-Fourier transform (Yang et al, 2013a), the Yang-Laplace transform (Zhao et al, 2014;Zhang et al, 2014) and variational homotopy perturbation method by (Noor and Mohyud-Din,2008). The variational homotopy perturbation method (VHPM) is a combination of the variational iteration method and homotopy perturbation method.…”