scholarly journals Analytical Solutions of the One-Dimensional Heat Equations Arising in Fractal Transient Conduction with Local Fractional Derivative

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Ai-Ming Yang ◽  
Carlo Cattani ◽  
Hossein Jafari ◽  
Xiao-Jun Yang
Keyword(s):  
Fractional Derivative ◽  
Analytical Solutions ◽  
Adomian Decomposition Method ◽  
Heat Equations ◽  
One Dimensional ◽  
Local Fractional Derivative ◽  
Adomian Decomposition ◽  
Local Fractional Calculus ◽  
Transient Conduction ◽  
The One

The one-dimensional heat equations with the heat generation arising in fractal transient conduction associated with local fractional derivative operators are investigated. Analytical solutions are obtained by using the local fractional Adomian decomposition method via local fractional calculus theory. The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.

scholarly journals Approximate analytical solutions of non-linear local fractional heat equations

2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 837-841 ◽  
Author(s):  
Shuxian Deng
Keyword(s):  
Analytical Solutions ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Heat Equations ◽  
Transform Method ◽  
Fractional Complex Transform ◽  
Fractional Heat Equation ◽  
Approximate Analytical Solutions ◽  
Adomian Decomposition ◽  
Non Linear

Consider the non-linear local fractional heat equation. The fractional complex transform method and the Adomian decomposition method are used to solve the equation. The approximate analytical solutions are obtained.

Analytical accuracy of the one dimensional heat transfer in geometry with logarithmic various surfaces

2014 ◽  
Vol 4 (4) ◽  
Author(s):  
A. Vahabzadeh ◽  
M. Fakour ◽  
D. Ganji ◽  
I. Rahimipetroudi
Keyword(s):  
Heat Transfer ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Physical Parameters ◽  
One Dimensional ◽  
Adomian Decomposition ◽  
Analytical Accuracy ◽  
Study Heat Transfer ◽  
The One

AbstractIn this study, heat transfer and temperature distribution equations for logarithmic surface are investigated analytically and numerically. Employing the similarity variables, the governing differential equations have been reduced to ordinary ones and solved via Homotopy perturbation method (HPM), Variational iteration method (VIM), Adomian decomposition method (ADM). The influence of the some physical parameters such as rate of effectiveness of temperature on non-dimensional temperature profiles is considered. Also the fourth-order Runge-Kutta numerical method (NUM) is used for the validity of these analytical methods and excellent agreement are observed between the solutions obtained from HPM, VIM, ADM and numerical results.

scholarly journals Approximation Solutions for Local Fractional Schrödinger Equation in the One-Dimensional Cantorian System

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yang Zhao ◽  
De-Fu Cheng ◽  
Xiao-Jun Yang
Keyword(s):  
Fractional Derivative ◽  
Series Expansion ◽  
Present Method ◽  
Expansion Method ◽  
One Dimensional ◽  
Local Fractional Derivative ◽  
Simple Tool ◽  
Fractional Schrödinger Equations ◽  
The One ◽  
Series Expansion Method

The local fractional Schrödinger equations in the one-dimensional Cantorian system are investigated. The approximations solutions are obtained by using the local fractional series expansion method. The obtained solutions show that the present method is an efficient and simple tool for solving the linear partial differentiable equations within the local fractional derivative.

scholarly journals Abundant Wave Accurate Analytical Solutions of the Fractional Nonlinear Hirota–Satsuma–Shallow Water Wave Equation

Fluids ◽  
2021 ◽  
Vol 6 (7) ◽  
pp. 235
Author(s):  
Chen Yue ◽  
Dianchen Lu ◽  
Mostafa M. A. Khater
Keyword(s):  
Wave Equation ◽  
Fractional Derivative ◽  
Shallow Water ◽  
Analytical Solutions ◽  
Water Wave ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Conformable Fractional Derivative ◽  
Adomian Decomposition ◽  
Fractional System

This research paper targets the fractional Hirota’s analytical solutions–Satsuma (HS) equations. The conformable fractional derivative is employed to convert the fractional system into a system with an integer–order. The extended simplest equation (ESE) and modified Kudryashov (MKud) methods are used to construct novel solutions of the considered model. The solutions’ accuracy is investigated by handling the computational solutions with the Adomian decomposition method. The solutions are explained in some different sketches to demonstrate more novel properties of the considered model.

scholarly journals Solving One Dimensional Ground Water Recharge Through Porous Media Using Elzaki Transform

2021 ◽  
pp. 370-376
Author(s):  
Krima B. Patel ◽  
Dr. Kamlesh A. Patel
Keyword(s):  
Porous Media ◽  
Ground Water ◽  
Decomposition Method ◽  
Graphical Representation ◽  
Adomian Decomposition Method ◽  
One Dimensional ◽  
Adomian Decomposition ◽  
Ground Water Recharge ◽  
Water Recharge ◽  
The One

In this paper, we have discussed the application of Elzaki Transform for finding the solution of One-Dimensional Ground Water Recharge through porous media. In this work, we present a reliable combination of Elaki transform and Adomian Decomposition method. The proposed method introduces Adomian polynomials and the nonlinear terms can be handled by the use of this polynomials easily. The Elaki Decomposition Method is used to solve the particular problem. The purpose of this method is to extend the application of Elzaki Decomposition Method. The proposed method worked perfectly to find the One-Dimensional Ground Water Recharge through porous media problem. We obtain numerical solution and graphical representation.

Nonlinear singular one dimensional thermo-elasticity coupled system and double Laplace decomposition methods

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6269-6280
Author(s):  
Hassan Gadain
Keyword(s):  
Laplace Transform ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Decomposition Methods ◽  
One Dimensional ◽  
Convergence Proof ◽  
Double Laplace Transform ◽  
Adomian Decomposition

In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.

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