In this paper, analytic solutions of two-dimensional coupled Burgers' equations are obtained by the Homotopy analysis and the Homotopy Pad$acute{e}$ methods. The obtained approximation by using Homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by $[m,m]$ Homotopy Pad$acute{e...

Given some type of fibration on a 4-manifold X with a torus regular fiber T , we may produce a new 4-manifold XT by performing torus surgery on T . There is a natural way to extend the fibration to XT , but a multiple fiber (nongeneric) singularity is introduced. We construct explicit generic fibrations (with only indefinite fold singularities) in a neighborhood of this multiple fiber. As an ap...

For spaces localized at 2, the classical EHP fibrations [1, 13] ΩS S ΩS ΩS play a crucial role for the computations of the homotopy groups of the spheres [16, 25]. The EHP-fibrations for (p− 1)-cell complexes for p > 2 are given in this article. These fibrations can be regarded as the odd prime analogue of the classical EHP-fibrations by considering the spheres as 1-cell complexes for p = 2. So...

We present a way of constructing a Quillen model structure on a full subcategory of an elementary topos, starting with an interval object with connections and a certain dominance. The advantage of this method is that it does not require the underlying topos to be cocomplete. The resulting model category structure gives rise to a model of homotopy type theory with identity types, Σand Π-types, a...

The linear homotopy theory for codifferential operator on Riemannian manifolds is developed in analogy to a similar idea exterior derivative. main object the cohomotopy operator, which singles out module of anticoexact forms from differential defined star-shaped open subset manifold. It shown that there direct sum decomposition form into coexact and anticoexat parts. This gives new way solving ...

This article presents an idea of a new approach for the solitary wave solution modified Degasperis–Procesi (mDP) and Camassa–Holm (mCH) models with time-fractional derivative. We combine Laplace transform (LT) homotopy perturbation method (HPM) to formulate (LHPTM). study is considered under Caputo sense. proposed strategy does not depend on any assumption restriction variables, such as in clas...

In this paper, we will study about Fractional-order partial differential equations in Mathematical Science and introduce analyse fractional calculus with an integral operator that contains the Caputo- Fabrizio’s fractional-order derivative. The advanced method is appropriate union of new transform named as ‘Mohand transform’ homotopy perturbation method. Some numerical examples are used to comm...

in this paper, elzaki homotopy perturbation method is employed for solving linear and nonlinear differential equations with a variable coffecient. this method is a combination of elzaki transform and homotopy perturbation method. the aim of using elzaki transform is to overcome the deficiencies that mainly caused by unsatised conditions in some semi-analytical methods such as homotopy perturbat...

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...

A smooth, projective surface S is called a standard isotrivial fibration if there exists a finite group G which acts faithfully on two smooth projective curves C1 and C2, so that S is isomorphic to the minimal desingularization of T := (C1 × C2)/G, where G acts diagonally on the product. When the action of G is free, then S = T is called a quasi-bundle. In this paper we analyse several numerica...