Efficient homotopy perturbation method for fractional non-linear equations using Sumudu transform

Homotopy Perturbation Sumudu Transform Method for Nonlinear Equations

In this paper, we propose a combined form of the sumudu transform method with the homotopy perturbation method to solve nonlinear equations. This method is called the homotopy perturbation sumudu transform method (HPSTM). The nonlinear terms can be easily handled by the use of He’s polynomials. The proposed scheme finds the solution without any discretization or restrictive assumptions and avoi...

Modified homotopy perturbation method for solving non-linear oscillator's ‎equations

In this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the Maclaurin series of the exact solution. Nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. These equations equip a significant mathematical model for dynamical systems. The accuracy o...

Homotopy Analysis Sumudu Transform Method for Nonlinear Equations

Homotopy Perturbation Method for Fractional Gas Dynamics Equation Using Sumudu Transform

and Applied Analysis 3 4. Solution by Homotopy Perturbation Sumudu Transform Method (HPSTM) 4.1. Basic Idea of HPSTM. To illustrate the basic idea of this method, we consider a general fractional nonlinear nonhomogeneous partial differential equationwith the initial condition of the form D α t U (x, t) + RU (x, t) + NU (x, t) = g (x, t) , (11) U (x, 0) = f (x) , (12) where Dα t U(x, t) is the C...

Variational Homotopy Perturbation Method for Linear Fractional Partial Differential Equations

In this article, the variational homotopy perturbation method (VHPM) [proposed in A. Noor et al., Mathematical Problems in Engineering, 1155(10) (2008), 696734] is adopted for solving linear fractional partial differential equations. The aim of this letter is to present an efficient and reliable treatment of the VHPM for the linear fractional partial differential equations. The fractional deriv...