The solution to a nonlinear equation is found in this study by combining classical and powerful method. Basically, it well known that the Homotopy Continuation Method (HCM) method has been used for solving problem of A new approach introduced which as Ostrowski (Ostrowski-HCM) with purpose overcome divergence arises from Ostrowski’s when bad initial guess used. To put simply, derivative given f...

The symmetry design of the system contains integer partial differential equations and fractional-order with fractional derivative. In this paper, we develop a scheme to examine shock wave occurring in motion gases Caputo sense. This is formulated using Mohand transform (MT) homotopy perturbation method (HPM), altogether called (MHPT). Our main finding paper handling recurrence relation that pro...

We construct compatible symplectic structures on manifolds Q3 × S1 for Waldhausen Q3 and show it is possible iff Q3 is a Stallings fibrations over S1. We describe bordisms of Lagrangian T 2-bundles over S1 × I .

We propose a notion of groupoid homotopy for generalized maps. This notion of groupoid homotopy generalizes the notions of natural transformation and strict homotopy for functors. The groupoid homotopy type of a Lie groupoid is shown to be invariant under Morita equivalence. As an application we consider orbifolds as groupoids and study the orbifold homotopy between orbifold maps induced by the...

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...

The homotopy perturbation method is a powerful device for solving a wide variety of problems arising in many scientific applications. In this paper, we investigate several integral equations by using T-stability of the Homotopy perturbation method investigates for solving integral equations. Some illustrative examples are presented to show that the Homotopy perturbation method is T-stable for s...

In this paper, Homotopy Analysis Method is used to analyze free non-linear vibrations of a beam simply supported by pinned ends under axial force. Mid-plane stretching is also considered for dynamic equation extracted for the beam. Galerkin decomposition technique is used to transform a partial dimensionless nonlinear differential equation of dynamic motion into an ordinary nonlinear differenti...

Analytical solutions are attractive for parametric studies and consideration of the problems physics. In addition, analytical solutions can be employed as a reference framewo...