In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution...

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.

In this work, the Blasius equation is studied. Homotopy perturbation method (HPM) and homotopy analysis method (HAM) are applied to obtain its solution. Comparison with variational iteration method (VIM) is made to highlight the significant features of employed methods and their capability of handling nonlinear problems. The outcome shows the success of (HPM) and (HAM) for solving nonlinear pro...

This paper presents the approximate solution of nonlinear acoustic wave propagation model is known as modified Camassa–Holm (mCH) equation with Caputo fractional derivative. We examine this study utilizing Laplace transform ( ℒ T) coupled homotopy perturbation method (HPM) to construct strategy id="M...

Through the use of a unique approach, we study fractional Biswas–Milovic model with Kerr and parabolic law nonlinearities in this paper. The Caputo approach is used to take derivative. method employed here homotopy perturbation transform (HPTM), which combines (HPM) Yang (YT). HPTM method, He’s polynomials, transform. polynomial wonderful tool for dealing nonlinear terms. To confirm validity ea...

This article uses the Yang transform decomposition method and homotopy perturbation to study seventh-order time-fractional Sawada–Kotera–Ito equation. The fractional derivative is taken into account in Caputo sense. We used with Adomian process procedure on problem obtain solution. looked at a single case contrasted it actual result validate methodologies. These techniques create recurrence rel...

We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. It was already shown in [1] that the inclusion of the first space into the second one is a homotopy equivalence. In this paper we prove that the homotopy types of the terms of the natural ‘degree’ filtration approximate closer and closer the homotopy type of the space o...

This paper proves that the functor C(∗) that sends pointed, simply-connected CW-complexes to their chain-complexes equipped with diagonals and iterated higher diagonals, determines their integral homotopy type — even inducing an equivalence of categories between the category of CW-complexes up to homotopy equivalence and a certain category of chain-complexes equipped with higher diagonals. Cons...