scholarly journals Fractional Telegraph Equation and Its Solution by Natural Transform Decomposition Method

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 334 ◽  
Author(s):  
Hassan Eltayeb ◽  
Yahya Abdalla ◽  
Imed Bachar ◽  
Mohamed Khabir
Keyword(s):  
Decomposition Method ◽  
Decomposition Methods ◽  
Telegraph Equation ◽  
Adomian Decomposition ◽  
Fractional Telegraph Equation ◽  
Telegraph Equations ◽  
Linear And Nonlinear

In this work, the natural transform decomposition method (NTDM) is applied to solve the linear and nonlinear fractional telegraph equations. This method is a combined form of the natural transform and the Adomian decomposition methods. In addition, we prove the convergence of our method. Finally, three examples have been employed to illustrate the preciseness and effectiveness of the proposed method.

scholarly journals An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 426 ◽  
Author(s):  
Hassan Khan ◽  
Rasool Shah ◽  
Poom Kumam ◽  
Dumitru Baleanu ◽  
Muhammad Arif
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Analytical Techniques ◽  
Telegraph Equation ◽  
High Rate ◽  
Analytical Technique ◽  
Decomposition Procedure ◽  
Adomian Decomposition ◽  
Telegraph Equations

In the present article, fractional-order telegraph equations are solved by using the Laplace-Adomian decomposition method. The Caputo operator is used to define the fractional derivative. Series form solutions are obtained for fractional-order telegraph equations by using the proposed method. Some numerical examples are presented to understand the procedure of the Laplace-Adomian decomposition method. As the Laplace-Adomian decomposition procedure has shown the least volume of calculations and high rate of convergence compared to other analytical techniques, the Laplace-Adomian decomposition method is considered to be one of the best analytical techniques for solving fractional-order, non-linear partial differential equations—particularly the fractional-order telegraph equation.

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.

Numerical Solution of Time-Fractional Klein–Gordon Equation by Using the Decomposition Methods

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Hossein Jafari
Keyword(s):  
Iterative Method ◽  
Numerical Solution ◽  
Decomposition Method ◽  
Gordon Equation ◽  
Adomian Decomposition Method ◽  
Type Equation ◽  
Decomposition Methods ◽  
Adomian Decomposition ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this paper, we apply two decomposition methods, the Adomian decomposition method (ADM) and a well-established iterative method, to solve time-fractional Klein–Gordon type equation. We compare these methods and discuss the convergence of them. The obtained results reveal that these methods are very accurate and effective.

scholarly journals Solving Some Linear and Nonlinear PDEs Using Laplace Adomian Decomposition Method

2018 ◽  
Vol 1 (2) ◽  
pp. 9-31
Author(s):  
Attaullah
Keyword(s):  
Decomposition Method ◽  
Evolution Equations ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Reaction Diffusion ◽  
Nonlinear Evolution Equations ◽  
Reaction Diffusion Equations ◽  
Nonlinear Pdes ◽  
Adomian Decomposition ◽  
Linear And Nonlinear

In this paper, Laplace Adomian decomposition method (LADM) is applied to solve linear and nonlinear partial differential equations (PDEs). With the help of proposed method, we handle the approximated analytical solutions to some interesting classes of PDEs including nonlinear evolution equations, Cauchy reaction-diffusion equations and the Klien-Gordon equations.

scholarly journals Solution of the space-fractional telegraph equations by using HAM

2015 ◽  
Vol 37 ◽  
pp. 320
Author(s):  
Mehdi Abedi-Varaki ◽  
Shahram Rajabi ◽  
Vahid Ghorbani ◽  
Farzad Hosseinzadeh
Keyword(s):  
Homotopy Analysis Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Analysis Method ◽  
Space And Time ◽  
Adomian Decomposition ◽  
Homotopy Analysis ◽  
Telegraph Equations

In this study by using the Homotopy Analysis Method (HAM) obtained approximate solutions for the space and time-fractional telegraph equations. In Caputo sense (Yildirim, 2010)these equations considered. Examples are solved and the obtained results show to be more accurate than Adomian Decomposition Method (ADM) and are more efficient and commodious.

scholarly journals A non-differentiable solution for the local fractional telegraph equation

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 225-231
Author(s):  
Jie Li ◽  
Ce Zhang ◽  
Weixing Liu ◽  
Yuzhu Zhang ◽  
Aimin Yang ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Fractional Derivative ◽  
Series Expansion ◽  
Expansion Method ◽  
Telegraph Equation ◽  
Differentiable Solution ◽  
Local Fractional Derivative ◽  
Fractional Telegraph Equation ◽  
Telegraph Equations ◽  
Series Expansion Method

In this paper, we consider the linear telegraph equations with local fractional derivative. The local fractional Laplace series expansion method is used to handle the local fractional telegraph equation. The analytical solution with the non-differentiable graphs is discussed in detail. The proposed method is efficient and accurate.

Numerical Solution of Space and Time Fractional Telegraph Equation: A Meshless Approach

2019 ◽  
Vol 20 (3-4) ◽  
pp. 325-337 ◽  
Author(s):  
Hitesh Bansu ◽  
Sushil Kumar
Keyword(s):  
Fractional Order ◽  
Kronecker Product ◽  
Fractional Derivatives ◽  
Telegraph Equation ◽  
New Approach ◽  
Numerical Examples ◽  
Novel Approach ◽  
Fractional Telegraph Equation ◽  
Precise Analysis ◽  
Telegraph Equations

AbstractIn recent years, there has been an incredible enthusiasm towards fractional order partial differential equations because of their incessant presence alongside different fields. Fractional derivatives offer an in-depth and precise analysis of the models of the systems. Particularly, fractional order telegraph equations (FOTE) have been taken into consideration and solved by plenty of researchers, using different techniques. In this paper, we present a novel approach and technique to solve fractional telegraph equation by fusion of cubic radial basis function and Chebyshev polynomials with the aid of Kronecker product. The numerical examples have been considered to verify the accuracy and also to demonstrate the performance of the new approach.

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