in this paper, we consider the variational homotopy perturbation method (vhpm) to obtain an approximate series solution for the generalized fisher’s equation which converges to the exact solution in the region of convergence. comparisons are made among the variational iteration method (vim), the exact solutions and the proposed method. the results reveal that the proposed method is very effectiv...

In this paper, we consider the inhomogeneous time-fractional nonlinear Fisher equation with three known boundary conditions. We first apply a modified Homotopy perturbation method for translating the proposed problem to a set of linear problems. Then we use the separation variables  method to solve obtained problems. In examples, we illustrate that by right choice of source term in the modified...

Homotopy type theory is a recent research area connecting type theory with homotopy theory by interpreting types as spaces. In particular, one can prove and mechanize type-theoretic analogues of homotopy-theoretic theorems, yielding “synthetic homotopy theory”. Here we consider the Seifert–van Kampen theorem, which characterizes the loop structure of spaces obtained by gluing. This is useful in...

In this paper, a Laplace transform decomposition algorithm (LTDA) is proposed to solve the Riccati equation. Comparisons are made among the homotopy perturbation method (HPM), the Adomian decomposition method (ADM) and the proposed method. It is shown that the homotopy perturbation method with a specific convex homotopy is equivalent to the Adomian decomposition method and the Laplace transform...

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

In this paper, we study semi-analytical methods entitled Homotopy pertourbation method (HPM) to solve fuzzy impulsive fractional differential equations based on the concept of generalized Hukuhara differentiability. At the end first of Homotopy pertourbation method is defined and its properties are considered completely. Then econvergence theorem for the solution are proved and we will show tha...

The homotopy analysis method is used to find a family of solitary smooth hump solutions of the Camassa–Holm equation. This approximate solution, which is obtained as a series of exponentials, agrees well with the known exact solution. This paper complements the work of Wu & Liao [Wu W, Liao S. Solving solitary waves with discontinuity by means of the homotopy analysis method. Chaos, Solitons & ...

In this work, we have applied Elzaki transform and He's homotopy perturbation method to solvepartial dierential equation (PDEs) with time-fractional derivative. With help He's homotopy per-turbation, we can handle the nonlinear terms. Further, we have applied this suggested He's homotopyperturbation method in order to reformulate initial value problem. Some illustrative examples aregiven in ord...