Elzaki Transform and the Decomposition Method for Nonlinear Fractional Partial Differential Equations

2016 ◽  
Vol 9 (4) ◽  
pp. 25-39
Author(s):  
Djelloul Ziane
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential

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 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 Fractional Variational Iteration Method versus Adomian’s Decomposition Method in Some Fractional Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Junqiang Song ◽  
Fukang Yin ◽  
Xiaoqun Cao ◽  
Fengshun Lu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Iteration Method ◽  
Decomposition Method ◽  
Variational Iteration Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Variational Iteration ◽  
Adomian’S Decomposition Method ◽  
Adomian’S Polynomials

A comparative study is presented about the Adomian’s decomposition method (ADM), variational iteration method (VIM), and fractional variational iteration method (FVIM) in dealing with fractional partial differential equations (FPDEs). The study outlines the significant features of the ADM and FVIM methods. It is found that FVIM is identical to ADM in certain scenarios. Numerical results from three examples demonstrate that FVIM has similar efficiency, convenience, and accuracy like ADM. Moreover, the approximate series are also part of the exact solution while not requiring the evaluation of the Adomian’s polynomials.

scholarly journals Exact Solution of Two-Dimensional Fractional Partial Differential Equations

2020 ◽  
Vol 4 (2) ◽  
pp. 21 ◽  
Author(s):  
Dumitru Baleanu ◽  
Hassan Kamil Jassim
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Approximate Solutions ◽  
Two Dimensional ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Sumudu Transform ◽  
Fractional Differential

In this study, we examine adapting and using the Sumudu decomposition method (SDM) as a way to find approximate solutions to two-dimensional fractional partial differential equations and propose a numerical algorithm for solving fractional Riccati equation. This method is a combination of the Sumudu transform method and decomposition method. The fractional derivative is described in the Caputo sense. The results obtained show that the approach is easy to implement and accurate when applied to various fractional differential equations.

scholarly journals Analytical Solution of Fractional-Order Hyperbolic Telegraph Equation, Using Natural Transform Decomposition Method

Electronics ◽  
2019 ◽  
Vol 8 (9) ◽  
pp. 1015 ◽  
Author(s):  
Hassan Khan ◽  
Rasool Shah ◽  
Dumitru Baleanu ◽  
Poom Kumam ◽  
Muhammad Arif
Keyword(s):  
Applied Sciences ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Decomposition Method ◽  
Telegraph Equation ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Present Technique ◽  
Telegraph Equations

In the current paper, fractional-order hyperbolic telegraph equations are considered for analytical solutions, using the decomposition method based on natural transformation. The fractional derivative is defined by the Caputo operator. The present technique is implemented for both fractional- and integer-order equations, showing that the current technique is an accurate analytical instrument for the solution of partial differential equations of fractional-order arising in all branches of applied sciences. For this purpose, several examples related to hyperbolic telegraph models are presented to explain the procedure of the suggested method. It is noted that the procedure of the present technique is simple, straightforward, accurate, and found to be a better mathematical technique to solve non-linear fractional partial differential equations.

scholarly journals Oscillation criteria of certain fractional partial differential equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Di Xu ◽  
Fanwei Meng
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Derivatives ◽  
Sufficient Conditions ◽  
Riccati Transformation ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Oscillation Criteria ◽  
Generalized Riccati Transformation

Abstract In this article, we regard the generalized Riccati transformation and Riemann–Liouville fractional derivatives as the principal instrument. In the proof, we take advantage of the fractional derivatives technique with the addition of interval segmentation techniques, which enlarge the manners to demonstrate the sufficient conditions for oscillation criteria of certain fractional partial differential equations.

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