The solution methods of nonlinear differential equations are very important because most of the physical phenomena are modelled by using such kind of equations. Therefore, this work presents a rational version of homotopy perturbation method RHPM as a novel tool with high potential to find approximate solutions for nonlinear differential equations. We present two case studies; for the first exa...

Although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. Some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.Here, after criticizi...

We use the q-homotopy analysis Shehu transform method in this article to obtain analytical and numerical solutions time fractional partial differential equations. also give two problems, as well a comparison study terms of absolute error with homotopy perturbation method, residual power series verify suggested technique’s effectiveness correctness. The graphical achieved by proposed show that i...