in this paper, nonlinear klein-gordon equation with quadratic term is solved by means of an analytic technique, namely the homotopy analysis method (ham).comparisons are made between the adomian decomposition method (adm), the exact solution and homotopy analysis method. the results reveal that the proposed method is very effective and simple.

Traditional Adomian decomposition method (ADM) usually fails to solve singular initial value problems of Emden-Fowler type. To overcome this shortcoming, a new and effective modification of ADM that only requires calculation of the first Adomian polynomial is formally proposed in the present paper. Three singular initial value problems of Emden-Fowler type with , 1 α  , 2 and , 2  and have be...

Abstract In this work, a coupled system of time-fractional modified Burgers’ equations is considered. Three different fractional operators: Caputo, Caputo-Fabrizio and Atangana-Baleanu operators are implemented for the equations. Also, two scenarios examined each operator: when initial conditions u(x, y, 0) = sin(xy), v(x, they e {−kxy} , where k, α some positive constants. With aid computable ...

A new technique of the Adomian decomposition method is developed and applied in this research article to solve two-term diffusion wave fractional telegraph equations with initial-boundary conditions. The proposed used problems both integer order equations. fractional-order solutions provide useful information about data transmission from one point another. are obtained form infinite series, dem...

In this manuscript, the nonlinear Burgers equations are studied via a fractal fractional (FF) Caputo operator. The results of coupled fixed point theorems in cone metric space used to discuss uniqueness solution proposed equations. equation is computed Natural transform associated with Adomian decomposition method (NADM). acquired graphically presented for some values order and dimensions. accu...

The fractional generalization of the Ambartsumian delay equation with Caputo’s derivative is considered. very difficult to be solved neither in case ordinary derivatives nor derivatives. In this paper we combine Laplace transform Adomian decomposition method solve studied equation. exact solution obtained as a series which terms are expressed by Mittag-Leffler functions. advantage present appro...

Adomian decomposition method has been applied to solve many functional equations so far. In this work, this method is applied to solve hyperbolic partial differential equations and results will be compared with characteristics method. 2004 Elsevier Inc. All rights reserved.

Abstract This paper presents the results of applying a new iterative method to linear and nonlinear fractional partial differential equations in fluid mechanics. A numerical analysis was performed find an exact solution wave equation Burgers’ equation, as well approximate KdV Boussinesq equation. Fractional derivatives order α are described using Caputo's definition with 0 < ≤ 1 or 2 . compa...

In this paper, the Adomian decomposition method for solving the linear and nonlinear parabolic equations is implemented with appropriate initial conditions. In comparison with existing techniques, the decomposition method is highly effective in terms of accuracy and rapid convergence. The numerical results obtained by this way have been compared with the exact solution to show the efficiency of...

The ideal magnetic flux-controlled memristor was introduced into a four-dimensional chaotic system and combined with fractional calculus theory, novel commensurate fractional-order proposed solved using the Adomian decomposition method. orders, parameters, initial values were studied as independent variables in bifurcation diagram Lyapunov exponents spectrum, it discovered that changing these c...