We extend the theory of Quillen adjunctions by combining ideas of homotopical algebra and of enriched category theory. Our results describe how the formulas for homotopy colimits of Bousfield and Kan arise from general formulas describing the derived functor of the weighted colimit functor.

The purpose of this paper is to show that ideas and techniques of the homotopy continuation method can be used to find the complete set of eigenpairs of a symmetric matrix. The homotopy defined by Chow, Mallet- Paret and York [I] may be used to solve this problem with 2""-n curves diverging to infinity which for large n causes a great inefficiency. M. Chu 121 introduced a homotopy equation...

A. Noor et al. [7] analyze a technique by combining the variational iteration method and the homotopy perturbation method which is called the variational homotopy perturbation method (VHPM) for solving higher dimensional initial boundary value problems. In this paper, we consider the VHPM to obtain exact solution to Gas Dynamics equation.

In this paper, we will compare a Homotopy perturbation algorithm and Taylor series expansin method for a system of second kind Fredholm integral equations. An application of He’s homotopy perturbation method is applied to solve the system of Fredholm integral equations. Taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

Abstract: In this paper, new algorithm of homotopy analysis method is successfully applied to obtain the approximate analytical solutions of the Cauchy reaction-diffusion equation. Reaction-diffusion equations have special importance in engineering and sciences and constitute a good model for many systems in various fields. Application of new algorithm of homotopy analysis method to this proble...

The aim of this paper is by using the fractional complex transform and the optimal homotopy analysis by method (OHAM) to find the analytical approximate solutions for nonlinear partial fractional differential Zakharov-Kuznetsov equation. Fractional complex transformation is proposed to convert nonlinear partial fractional differential Zakharov-Kuznetsov equation to nonlinear partial differentia...