scholarly journals On the Inverse Problem of the Fractional Heat-Like Partial Differential Equations: Determination of the Source Function

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Gülcan Özkum ◽  
Ali Demir ◽  
Sertaç Erman ◽  
Esra Korkmaz ◽  
Berrak Özgür
Keyword(s):  
Differential Equation ◽  
Inverse Problem ◽  
Variable Coefficient ◽  
Decomposition Method ◽  
Source Function ◽  
Adomian Decomposition Method ◽  
Diffusion Equations ◽  
Adomian Decomposition ◽  
Fractional Differential

The study in this paper mainly concerns the inverse problem of determining an unknown source function in the linear fractional differential equation with variable coefficient using Adomian decomposition method (ADM). We apply ADM to determine the continuous right hand side functionsfxandftin the heat-like diffusion equationsDtαux,t=hxuxxx,t+fxandDtαux,t=hxuxxx,t+ft, respectively. The results reveal that ADM is very effective and simple for the inverse problem of determining the source function.

scholarly journals The source function of fractional heat-like systems

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1683-1688
Author(s):  
Ying-Xin Guo ◽  
Rui-Yuan Zhu ◽  
Shu-Lan Kong ◽  
Jing-Dong Zhao
Keyword(s):  
Inverse Problem ◽  
Variable Coefficient ◽  
Decomposition Method ◽  
Source Function ◽  
Adomian Decomposition Method ◽  
Unknown Source ◽  
Adomian Decomposition

In this paper, we study the inverse problem for seeking an unknown source function of the linear fractional heat systems with variable coefficient using Adomian decomposition method. The results prove that Adomian decomposition method is very effective and simple for the inverse problem of finding the source function of the heat systems.

scholarly journals Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Veyis Turut ◽  
Nuran Güzel
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Power Series ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Fractional Differential

Two tecHniques were implemented, the Adomian decomposition method (ADM) and multivariate Padé approximation (MPA), for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM), then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.

scholarly journals Solution to the Linear Fractional Differential Equation Using Adomian Decomposition Method

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Jin-Fa Cheng ◽  
Yu-Ming Chu
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Fractional Derivative ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Initial Value ◽  
Adomian Decomposition ◽  
Constant Coefficients ◽  
Fractional Differential ◽  
Linear Fractional Differential Equations

We obtain the analytical general solution of the linear fractional differential equations with constant coefficients by Adomian decomposition method under nonhomogeneous initial value condition, which is in the sense of the Caputo fractional derivative.

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 Analytical Solutions of Fractional Differential Equations Using the Convenient Adomian Series

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Xiang-Chao Shi ◽  
Lan-Lan Huang ◽  
Zhen-Guo Deng ◽  
Dan Liu
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Decomposition Method ◽  
Order Approximation ◽  
Adomian Decomposition Method ◽  
Higher Order ◽  
Nonlinear Fractional Differential Equation ◽  
Adomian Decomposition ◽  
Engineering Problems ◽  
Fractional Differential

Due to the memory trait of the fractional calculus, numerical or analytical solution of higher order becomes very difficult even impossible to obtain in real engineering problems. Recently, a new and convenient way was suggested to calculate the Adomian series and the higher order approximation was realized. In this paper, the Adomian decomposition method is applied to nonlinear fractional differential equation and the error analysis is given which shows the convenience.

scholarly journals Solution of an extraordinary differential equation by Adomian decomposition method

2004 ◽  
Vol 2004 (4) ◽  
pp. 331-338 ◽  
Author(s):  
S. Saha Ray ◽  
R. K. Bera
Keyword(s):  
Differential Equation ◽  
Laplace Transform ◽  
Fractional Differential Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Alternative Method ◽  
Adomian Decomposition ◽  
Fractional Differential

The aim of the present analysis is to apply the Adomian decomposition method for the solution of a fractional differential equation as an alternative method of Laplace transform.

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