Homotopy perturbation method for fractional Fornberg–Whitham equation

Feng’s First Integral Method Applied to the ZKBBM and the Generalized Fisher Space-Time Fractional Equations

“…Recently, a large amount of literature has been provided to construct the solutions of fractional ordinary differential equations, fractional partial differential equations (PDEs), and integral equations of physical interest. Several powerful methods have been proposed to obtain approximate and exact solutions of fractional differential equations, such as the Adomian decomposition method [4,5], the variational iteration method [6][7][8], the homotopy analysis method [9][10][11][12], the homotopy perturbation method [13][14][15], the Lagrange characteristic method [16], and the fractional subequation method [17].…”

Reliable analysis for time-fractional nonlinear differential difference equations

“…Singh et al [20] used the HPM to determine solutions of space-time fractional solidification in a finite slab in 2010. Recently, Gupta and Singh [21] have determined the approximate solution of time-fractional Fornberg-Whitham equation by HPM. In this article, we implement the Homotopy perturbation method for obtaining an analytical solution of timefractional nonlinear differential difference equation, namely, the hybrid equation, the Toda lattice equation and the relativistic Toda lattice difference equation.…”

On the Closed Form Solutions of Linear and Nonlinear Cauchy Reaction-Diffusion Equations Using the Hybrid of Fourier Transform and Variational Iteration Method

“…Moreover, due to the non-linear nature and variable coefficients of these differential equations, attentions are devoted to the approximate solutions obtained by semi analytical methods such as the Homotopy Perturbation Method (HPM) (He, 2009;Kasozi et al, 2011;Gupta and Singh, 2011;Othman et al, 2010;Gepreel, 2011;Aslanov, 2011) and Variational Iteration Method (VIM) (He et al, 2010;Shakeri, et al, 2009;Chen and Wang, 2010;Zhou and Yao, 2010;Odibat, 2010;Zhao and Xiao, 2010;Shang and Han, 2010;Turkyilmazoglu, 2011). The VIM is developed by employing a correction functional and a general Lagrange multiplier for the differential equation.…”

“…However, the solutions of these problems are valid only in onedirectional problem domain either in time or space problem domain. In other words, the unsatisfied boundary conditions in the solutions of the VIM and other semi-analytical methods play no role in the final results (Kasozi et al, 2011;Gupta and Singh, 2011;Othman et al, 2010;Gepreel, 2011;Aslanov, 2011;Madani et al, 2011;He et al, 2010;Chen and Wang, 2010;Zhou and Yao, 2010;Odibat, 2010;Zhao and Xiao, 2010;Shang and Han, 2010;Turkyilmazoglu, 2011;Afshari et al, 2009;Aruchunan and Sulaiman, 2010). Therefore, there has been a deficiency as a built in short comes in the solutions using the VIM and other semi-analytical methods.…”