ANALYTICAL APPROXIMATION SOLUTION OF SYSTEM OF PSEUDO-PARABOLIC FRACTIONAL EQUATIONS USING A MODIFIED DOUBLE LAPLACE DECOMPOSITION METHOD

2020 ◽  
Vol 19 (2) ◽  
pp. 167-190
Author(s):  
Soampa Bangan ◽  
Djibibe Moussa Zakari
Keyword(s):  
Decomposition Method ◽  
Analytical Approximation ◽  
Approximation Solution ◽  
Fractional Equations ◽  
Laplace Decomposition Method

scholarly journals On a nonlinear singular one-dimensional parabolic equation and double Laplace decomposition method

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668653 ◽  
Author(s):  
Hassan Eltayeb Gadain ◽  
Imed Bachar
Keyword(s):  
Parabolic Equation ◽  
Laplace Transform ◽  
Convergence Analysis ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
One Dimensional ◽  
Double Laplace Transform ◽  
Adomian Decomposition ◽  
Laplace Decomposition Method

In this article, the double Laplace transform and Adomian decomposition method are used to solve the nonlinear singular one-dimensional parabolic equation. In addition, we studied the convergence analysis of our problem. Using two examples, our proposed method is illustrated and the obtained results are confirmed.

scholarly journals Approximate Solutions of the Damped Wave Equation and Dissipative Wave Equation in Fractal Strings

2019 ◽  
Vol 3 (2) ◽  
pp. 26 ◽  
Author(s):  
Dumitru Baleanu ◽  
Hassan Kamil Jassim
Keyword(s):  
Wave Equation ◽  
Decomposition Method ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Damped Wave Equation ◽  
Fractal Strings ◽  
Fractional Derivative Operators ◽  
Laplace Decomposition Method ◽  
Dissipative Wave Equation

In this paper, we apply the local fractional Laplace variational iteration method (LFLVIM) and the local fractional Laplace decomposition method (LFLDM) to obtain approximate solutions for solving the damped wave equation and dissipative wave equation within local fractional derivative operators (LFDOs). The efficiency of the considered methods are illustrated by some examples. The results obtained by LFLVIM and LFLDM are compared with the results obtained by LFVIM. The results reveal that the suggested algorithms are very effective and simple, and can be applied for linear and nonlinear problems in sciences and engineering.

scholarly journals A Note on Double Conformable Laplace Transform Method and Singular One Dimensional Conformable Pseudohyperbolic Equations

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 949 ◽  
Author(s):  
Hassan Eltayeb ◽  
Said Mesloub ◽  
Yahya T. Abdalla ◽  
Adem Kılıçman
Keyword(s):  
Present Method ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
High Accuracy ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Numerical Examples ◽  
One Dimensional ◽  
Linear And Nonlinear ◽  
Laplace Decomposition Method

The purpose of this article is to obtain the exact and approximate numerical solutions of linear and nonlinear singular conformable pseudohyperbolic equations and conformable coupled pseudohyperbolic equations through the conformable double Laplace decomposition method. Further, the numerical examples were provided in order to demonstrate the efficiency, high accuracy, and the simplicity of present method.

Numerical simulation of the fractional Lienard’s equation

2019 ◽  
Vol 30 (3) ◽  
pp. 1223-1232 ◽  
Author(s):  
Razan Alchikh ◽  
Suheil Khuri
Keyword(s):  
Decomposition Method ◽  
Design Methodology ◽  
Nonlinear Term ◽  
Initial Conditions ◽  
Recursive Algorithm ◽  
Content Type ◽  
Fractional Differential ◽  
Laplace Decomposition Method ◽  
First Time

Purpose The purpose of this paper is to apply an efficient semi-analytical method for the approximate solution of Lienard’s equation of fractional order. Design/methodology/approach A Laplace decomposition method (LDM) is implemented for the nonlinear fractional Lienard’s equation that is complemented with initial conditions. The nonlinear term is decomposed and then a recursive algorithm is constructed for the determination of the proposed infinite series solution. Findings A number of examples are tested to explicate the efficiency of the proposed technique. The results confirm that this approach is convergent and highly accurate by using only few iterations of the proposed scheme. Originality/value The approach is original and is of value because it is the first time that this approach is used successfully to tackle fractional differential equations, which are of great interest for authors in the recent years.

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