scholarly journals Homotopy Perturbation Elzaki Transform Method for Obtaining the Approximate Solutions of the Random Partial Differential Equations

2021 ◽  
Author(s):  
Halil ANAÇ ◽  
Mehmet MERDAN ◽  
Tülay KESEMEN
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Approximate Solutions ◽  
Partial Differential ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Random Partial Differential Equations

Analytical Approach to Time-Fractional Partial Differential Equations in Fluid Mechanics

2011 ◽  
Vol 347-353 ◽  
pp. 463-466
Author(s):  
Xue Hui Chen ◽  
Liang Wei ◽  
Lian Cun Zheng ◽  
Xin Xin Zhang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fluid Mechanics ◽  
Approximate Solutions ◽  
Differential Transform Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Differential Transform ◽  
Generalized Differential

The generalized differential transform method is implemented for solving time-fractional partial differential equations in fluid mechanics. This method is based on the two-dimensional differential transform method (DTM) and generalized Taylor’s formula. Results obtained by using the scheme presented here agree well with the numerical results presented elsewhere. The results reveal the method is feasible and convenient for handling approximate solutions of time-fractional partial differential equations.

Homotopy Perturbation Transform Method with He’s Polynomial for Solution of Coupled Nonlinear Partial Differential Equations

2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Dinkar Sharma ◽  
Prince Singh ◽  
Shubha Chauhan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equations ◽  
Two Dimensions ◽  
Partial Differential ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
The Laplace Transform

AbstractIn this paper, a combined form of the Laplace transform method with the homotopy perturbation method (HPTM) is applied to solve nonlinear systems of partial differential equations viz. the system of third order KdV Equations and the systems of coupled Burgers’ equations in one- and two- dimensions. The nonlinear terms can be easily handled by the use of He’s polynomials. The results shows that the HPTM is very efficient, simple and avoids the round-off errors. Four test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM) which shows that this method is a suitable method for solving systems of partial differential equations.

scholarly journals Fractional View Analysis of Acoustic Wave Equations, Using Fractional-Order Differential Equations

2020 ◽  
Vol 10 (2) ◽  
pp. 610 ◽  
Author(s):  
Izaz Ali ◽  
Hassan Khan ◽  
Rasool Shah ◽  
Dumitru Baleanu ◽  
Poom Kumam ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Wave ◽  
Fractional Order ◽  
Wave Equations ◽  
Research Work ◽  
Analytical Techniques ◽  
Partial Differential ◽  
Transform Method ◽  
Homotopy Perturbation

In the present research work, a newly developed technique which is known as variational homotopy perturbation transform method is implemented to solve fractional-order acoustic wave equations. The basic idea behind the present research work is to extend the variational homotopy perturbation method to variational homotopy perturbation transform method. The proposed scheme has confirmed, that it is an accurate and straightforward technique to solve fractional-order partial differential equations. The validity of the method is verified with the help of some illustrative examples. The obtained solutions have shown close contact with the exact solutions. Furthermore, the highest degree of accuracy has been achieved by the suggested method. In fact, the present method can be considered as one of the best analytical techniques compared to other analytical techniques to solve non-linear fractional partial differential equations.

scholarly journals A new modified homotopy perturbation method for fractional partial differential equations with proportional delay

2020 ◽  
Vol 19 ◽  
pp. 58-73
Author(s):  
Ahmad. A. H. Mtawal ◽  
Sameehah. R. Alkaleeli
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Proportional Delay ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Homotopy Perturbation

In this paper, we suggest and analyze a technique by combining the Shehu transform method and the homotopy perturbation method. This method is called the Shehu transform homotopy method (STHM). This method is used to solve the time-fractional partial differential equations (TFPDEs) with proportional delay. The fractional derivative is described in Caputo's sense. The solutions proposed in the series converge rapidly to the exact solution. Some examples are solved to show the STHM is easy to apply.

scholarly journals Effective Method for Solving Different Types of Nonlinear Fractional Burgers’ Equations

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 729 ◽  
Author(s):  
Safyan Mukhtar ◽  
Salah Abuasad ◽  
Ishak Hashim ◽  
Samsul Ariffin Abdul Karim
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Approximate Solutions ◽  
Three Dimensions ◽  
Partial Differential ◽  
Transform Method ◽  
Burgers Equations ◽  
Different Types ◽  
In Series

In this study, a relatively new method to solve partial differential equations (PDEs) called the fractional reduced differential transform method (FRDTM) is used. The implementation of the method is based on an iterative scheme in series form. We test the proposed method to solve nonlinear fractional Burgers equations in one, two coupled, and three dimensions. To show the efficiency and accuracy of this method, we compare the results with the exact solutions, as well as some established methods. Approximate solutions for different values of fractional derivatives together with exact solutions and absolute errors are represented graphically in two and three dimensions. From all numerical results, we can conclude the efficiency of the proposed method for solving different types of nonlinear fractional partial differential equations over existing methods.

scholarly journals A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Shehu Maitama
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Analytical Method ◽  
Homotopy Perturbation Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear

A hybrid analytical method for solving linear and nonlinear fractional partial differential equations is presented. The proposed analytical approach is an elegant combination of the Natural Transform Method (NTM) and a well-known method, Homotopy Perturbation Method (HPM). In this analytical method, the fractional derivative is computed in Caputo sense and the nonlinear term is calculated using He’s polynomial. The proposed analytical method reduces the computational size and avoids round-off errors. Exact solution of linear and nonlinear fractional partial differential equations is successfully obtained using the analytical method.

An efficient hybrid computational technique for solving nonlinear local fractional partial differential equations arising in fractal media

2018 ◽  
Vol 7 (3) ◽  
pp. 229-235 ◽  
Author(s):  
Amit Prakash ◽  
Hardish Kaur
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Planck Equation ◽  
Computational Technique ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Fractal Media ◽  
Sumudu Transform

AbstractIn present work, nonlinear fractional partial differential equations namely transport equation and Fokker-Planck equation involving local fractional differential operators, are investigated by means of the local fractional homotopy perturbation Sumudu transform method. The proposed method is a coupling of homotopy perturbation method with local fractional Sumudu transform and is used to describe the non-differentiable problems. Numerical simulation results are projected to show the efficiency of the proposed technique.

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.

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