scholarly journals Solution of Space-Time-Fractional Problem by Shehu Variational Iteration Method

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Suleyman Cetinkaya ◽  
Ali Demir ◽  
Hulya Kodal Sevindir
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Iteration Method ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
Space Time ◽  
Variational Iteration ◽  
Mathematical Problems ◽  
Fractional Differential ◽  
Time Fractional Differential Equations

In this study, we deal with the problem of constructing semianalytical solution of mathematical problems including space-time-fractional linear and nonlinear differential equations. The method, called Shehu Variational Iteration Method (SVIM), applied in this study is a combination of Shehu transform (ST) and variational iteration method (VIM). First, ST is utilized to reduce the time-fractional differential equation with fractional derivative in Liouville-Caputo sense into an integer-order differential equation. Later, VIM is implemented to construct the solution of reduced differential equation. The convergence analysis of this method and illustrated examples confirm that the proposed method is one of best procedures to tackle space-time-fractional differential equations.

scholarly journals Solusi Persamaan Diferensial Fraksional Riccati Menggunakan Adomian Decomposition Method dan Variational Iteration Method

Matematika ◽  
2019 ◽  
Vol 18 (1) ◽  
Author(s):  
Muhamad Deni Johansyah ◽  
Herlina Napitupulu ◽  
Erwin Harahap ◽  
Ira Sumiati ◽  
Asep K. Supriatna
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Iteration Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Adomian Decomposition ◽  
Fractional Differential

Abstrak. Pada umumnya orde dari persamaan diferensial adalah bilangan asli, namun orde pada persamaan diferensial dapat dibentuk menjadi orde pecahan yang disebut persamaan diferensial fraksional. Paper ini membahas persamaan diferensial fraksional Riccati dengan orde diantara nol dan satu, dan koefisien konstan. Metode numerik yang digunakan untuk mendapatkan solusi dari persamaan diferensial fraksional Riccati adalah Adomian Decomposition Method (ADM) dan Variational Iteration Method (VIM). Tujuan dari paper ini adalah untuk memperluas penerapan ADM dan VIM dalam menyelesaikan persamaan diferensial fraksional Riccati nonlinear dengan turunan Caputo. Perbandingan solusi yang diperoleh menunjukkan bahwa VIM adalah metode yang lebih sederhana untuk mencari solusi persamaan diferensial fraksional Riccati nonlinier dengan orde antara nol dan satu, kemudian hasil yang diperoleh disajikan dalam bentuk grafik.Kata kunci: diferensial, fraksional, riccati, adomian dekomposisiThe solution of Riccati Fractional Differential Equation using Adomian Decomposition methodAbstract. Generally, the order of differential equations is a natural numbers, but this order can be formed into fractional, called as fractional differential equations.  In this paper, the Riccati fractional differential equations with order between zero and one, and constant coefficient is discussed.  The numerical methods used to obtain solutions from Riccati fractional differential equations are the Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM).  The aim of this paper is to expand the application of ADM and VIM in solving nonlinear Riccati fractional differential equations with Caputo derivatives.  The comparison of the obtained solutions shows that VIM is simpler method for finding solutions to Riccati nonlinear fractional differential equations with order between zero and one. The obtained results are presented graphically.Keywords: riccati, fractional, differential, adomian, decomposition

scholarly journals On the Solution of Local Fractional Differential Equations Using Local Fractional Laplace Variational Iteration Method

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Pranay Goswami ◽  
Rubayyi T. Alqahtani
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Differential Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Telegraph Equation ◽  
Space Time ◽  
Variational Iteration ◽  
Fractional Differential ◽  
Fractional Space

We present iteration formulae of a fractional space-time telegraph equation using the combination of fractional variational iteration method and local fractional Laplace transform.

Solve fractional differential equations via a hybrid method between variational iteration method and gray wolf optimization algorithm

2020 ◽  
pp. 2150144
Author(s):  
Ahmed Entesar ◽  
Omar Saber Qasim
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Hybrid Method ◽  
Optimization Algorithm ◽  
Iteration Method ◽  
Optimal Parameter ◽  
Variational Iteration Method ◽  
Gray Wolf ◽  
Variational Iteration ◽  
Fractional Differential

In this paper, a hybrid method between Variational Iteration Method (VIM) and gray wolf optimization algorithm (GWO) was proposed to solve the fractional differential equations (FDE), where the optimal parameter value ([Formula: see text] for the VIM was estimated by the GWO. The solutions in the proposed method, GWO-VIM, demonstrated the efficiency and reliability compared to the default method VIM, by calculating the maximum absolute errors (MAE) and mean square error (MSE).

scholarly journals New analytical solution for natural convection of Darcian fluid in porous media prescribed surface heat flux

2011 ◽  
Vol 15 (suppl. 2) ◽  
pp. 221-227 ◽  
Author(s):  
Domiry Ganji ◽  
Hasan Sajjadi
Keyword(s):  
Heat Flux ◽  
Porous Media ◽  
Differential Equations ◽  
Iteration Method ◽  
Surface Heat Flux ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
Surface Heat ◽  
Variational Iteration ◽  
He’S Variational Iteration Method

A new analytical method called He's Variational Iteration Method is introduced to be applied to solve nonlinear equations. In this method, general Lagrange multipliers are introduced to construct correction functional for the problems. It is strongly and simply capable of solving a large class of linear or nonlinear differential equations without the tangible restriction of sensitivity to the degree of the nonlinear term and also is very user friend because it reduces the size of calculations besides; its iterations are direct and straightforward. In this paper the powerful method called Variational Iteration Method is used to obtain the solution for a nonlinear Ordinary Differential Equations that often appear in boundary layers problems arising in heat and mass transfer which these kinds of the equations contain infinity boundary condition. The boundary layer approximations of fluid flow and heat transfer of vertical full cone embedded in porous media give us the similarity solution for full cone subjected to surface heat flux boundary conditions. The obtained Variational Iteration Method solution in comparison with the numerical ones represents a remarkable accuracy.

scholarly journals A New Approach for the Approximate Analytical Solution of Space-Time Fractional Differential Equations by the Homotopy Analysis Method

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Ali Demir ◽  
Mine Aylin Bayrak ◽  
Ebru Ozbilge
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Homotopy Analysis Method ◽  
Space Time ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Fractional Differential ◽  
Time Fractional Differential Equations

The motivation of this study is to construct the truncated solution of space-time fractional differential equations by the homotopy analysis method (HAM). The first space-time fractional differential equation is transformed into a space fractional differential equation or a time fractional differential equation before the HAM. Then the power series solution is constructed by the HAM. Finally, taking the illustrative examples into consideration we reach the conclusion that the HAM is applicable and powerful technique to construct the solution of space-time fractional differential equations.

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