“…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.…”