scholarly journals Yang-Laplace Decomposition Method for Nonlinear System of Local Fractional Partial Differential Equations

2019 ◽  
Vol 4 (2) ◽  
pp. 489-502 ◽  
Author(s):  
Djelloul Ziane ◽  
Mountassir Hamdi Cherif ◽  
Carlo Cattani ◽  
Kacem Belghaba
Keyword(s):  
Partial Differential Equations ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Decomposition Method ◽  
Differential Operators ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Computational Work ◽  
Laplace Decomposition Method

AbstractThe basic motivation of the present study is to extend the application of the local fractional Yang-Laplace decomposition method to solve nonlinear systems of local fractional partial differential equations. The differential operators are taken in the local fractional sense. The local fractional Yang-Laplace decomposition method (LFLDM) can be easily applied to many problems and is capable of reducing the size of computational work to find non-differentiable solutions for similar problems. Two illustrative examples are given, revealing the effectiveness and convenience of the method.

scholarly journals Improvement of the Modified Decomposition Method for Handling Third-Order Singular Nonlinear Partial Differential Equations with Applications in Physics

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Nemat Dalir
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Differential Operators ◽  
Nonlinear Partial Differential Equations ◽  
Initial Value ◽  
Third Order ◽  
Partial Differential ◽  
The Third

The modified decomposition method (MDM) is improved by introducing new inverse differential operators to adapt the MDM for handling third-order singular nonlinear partial differential equations (PDEs) arising in physics and mechanics. A few case-study singular nonlinear initial-value problems (IVPs) of third-order PDEs are presented and solved by the improved modified decomposition method (IMDM). The solutions are compared with the existing exact analytical solutions. The comparisons show that the IMDM is effectively capable of obtaining the exact solutions of the third-order singular nonlinear IVPs.

Numerical Solution of Fractional Partial Differential Equations by Discrete Adomian Decomposition Method

2014 ◽  
Vol 6 (01) ◽  
pp. 107-119 ◽  
Author(s):  
D. B. Dhaigude ◽  
Gunvant A. Birajdar
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Diffusion Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Discrete Schrödinger Equation ◽  
Adomian Decomposition

AbstractIn this paper we find the solution of linear as well as nonlinear fractional partial differential equations using discrete Adomian decomposition method. Here we develop the discrete Adomian decomposition method to find the solution of fractional discrete diffusion equation, nonlinear fractional discrete Schrodinger equation, fractional discrete Ablowitz-Ladik equation and nonlinear fractional discrete Burger’s equation. The obtained solution is verified by comparison with exact solution whenα= 1.

scholarly journals Application of Sumudu Decomposition Method to Solve Nonlinear System of Partial Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Hassan Eltayeb ◽  
Adem Kılıçman
Keyword(s):  
Partial Differential Equations ◽  
Nonlinear System ◽  
Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Partial Differential ◽  
Adomian Polynomials ◽  
Adomian Decomposition ◽  
Sumudu Transform

We develop a method to obtain approximate solutions of nonlinear system of partial differential equations with the help of Sumudu decomposition method (SDM). The technique is based on the application of Sumudu transform to nonlinear coupled partial differential equations. The nonlinear term can easily be handled with the help of Adomian polynomials. We illustrate this technique with the help of three examples, and results of the present technique have close agreement with approximate solutions obtained with the help of Adomian decomposition method (ADM).

Transformations of Nonlinear Systems to High-Order Generalized Chained Forms

2004 ◽  
Vol 127 (4) ◽  
pp. 729-733 ◽  
Author(s):  
Maria-Christina Laiou ◽  
Alessandro Astolfi
Keyword(s):  
Partial Differential Equations ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
High Order ◽  
Partial Differential ◽  
Stabilization Methods ◽  
Surface Vessel

A variety of stabilization methods for nonlinear systems in chained form can be found in the literature. However, very few results exist in the area of systematically converting a general nonlinear system with two inputs to a chained form. This paper presents an algorithm for the conversion of a class of nonlinear systems with two inputs to a high-order chained, or generalized chained, form. The feedback transformation accomplishing this conversion is derived, provided certain conditions hold, by solving a system of partial differential equations. The proposed algorithm is illustrated by means of a physically motivated example, namely an under-actuated surface vessel.

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