In this paper, a coupling method of a homotopy technique and a perturbation technique is proposed to solve non-linear problems. In contrast to the traditional perturbation methods, the proposed method does not require a small parameter in the equation. In this method, according to the homotopy technique, a homotopy with an imbedding parameter p3[0, 1] is constructed, and the imbedding parameter...

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...

This paper focuses on solving the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation (FCDGSKE). We propose two analytical methods based complex transform, variational iteration method and homotopy perturbation method. The approximated solutions to initial value problems associated with FCDGSKE are provided without linearization complicated calculation. Numerical results show main merits...

In this paper, a homotopy perturbation method (HPM) and modified homotopy perturbation (MHPM) are proposed to solve singular integral equation with generalized Abel's kernel.

This paper has applied a hybrid method called the homotopy perturbation transformation technique to solve fractional-order Newell-Whitehead-Segel equations. First, we used Yang given problem, and then, was implemented complete procedure of suggested method. The proposed is simplified requires small calculation achieve solution targeted problem. Moreover, derived results are in close contact wit...

In this manuscript, a new hybrid technique viz Sawi transform-based homotopy perturbation method is implemented to solve one-dimensional shallow water wave equations. general, the quantities involved with such equations are commonly assumed be crisp, but parameters in actual scenario may imprecise/uncertain. Therefore, fuzzy uncertainty introduced as an initial condition. The main focus of stud...

In this paper, we have applied the homotopy perturbation method (HPM) for obtaining the analytical solution of unsteady flow of gas through a porous medium and we have also compared the findings of this research with some other analytical results. Results showed a very good agreement between results of HPM and the numerical solutions of the problem rather than other analytical solutions which h...

Nonlinear partial differential equations are useful in describing the various phenomena in disciplines. The Homotopy perturbation method, first proposed by He in 1998, was developed and improved by He [5, 6, 7, 8]. Homotopy perturbation method [4] is a novel and effective method, and can solve various nonlinear equations. This method has been successfully applied to solve many types of nonlinea...