Numerical Solutions of Linear Time-fractional Klein-Gordon Equation by Using Power Series Approach

2018 ◽  
Author(s):  
Mohammad Alaroud ◽  
Mohammed Al-Smadi ◽  
Omar Abu Arqub ◽  
Rokiah Rozita Ahmad ◽  
Shaher Momani
Keyword(s):  
Power Series ◽  
Gordon Equation ◽  
Numerical Solutions ◽  
Linear Time ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals Time-Fractional Klein–Gordon Equation with Solitary/Shock Waves Solutions

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Sayed Saifullah ◽  
Amir Ali ◽  
Muhammad Irfan ◽  
Kamal Shah
Keyword(s):  
Laplace Transform ◽  
Decomposition Method ◽  
Wave Amplitude ◽  
Gordon Equation ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Double Laplace Transform ◽  
Proposed Model ◽  
Klein Gordon ◽  
Klein Gordon Equation

In this article, we study the time-fractional nonlinear Klein–Gordon equation in Caputo–Fabrizio’s sense and Atangana–Baleanu–Caputo’s sense. The modified double Laplace transform decomposition method is used to attain solutions in the form of series of the proposed model under aforesaid fractional operators. The suggested method is the composition of the double Laplace transform and decomposition method. The convergence of the considered method is demonstrated for the considered model. It is observed that the obtained solutions converge to the exact solution of the proposed model. For validity, we consider two particular examples with appropriate initial conditions and derived the series solution in the sense of both operators for the considered model. From numerical solutions, it is observed that the considered model admits pulse-shaped solitons. It is also observed that the wave amplitude enhances with variations in time, which infers the coefficient α significantly increases the wave amplitude and affects the nonlinearity/dispersion effects, therefore may admit monotonic shocks. The physical behavior of the considered numerical examples is illustrated explicitly which reveals the evolution of localized shock excitations.

Higher-Order Numerical Solutions of a 2+1d Nonlinear Klein-Gordon Equation

1989 ◽  
Vol 58 (10) ◽  
pp. 3509-3513 ◽  
Author(s):  
Hideo Fusaoka
Keyword(s):  
Gordon Equation ◽  
Numerical Solutions ◽  
Higher Order ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals Numerical solution of the linear time fractional Klein-Gordon equation using transform based localized RBF method and quadrature

2020 ◽  
Vol 5 (5) ◽  
pp. 5287-5308
Author(s):  
Xiangmei Li ◽  
◽  
Kamran ◽  
Absar Ul Haq ◽  
Xiujun Zhang ◽  
...  
Keyword(s):  
Numerical Solution ◽  
Gordon Equation ◽  
Linear Time ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals Analysis of nonlinear time-fractional Klein-Gordon equation with power law kernel

2022 ◽  
Vol 7 (4) ◽  
pp. 5275-5290
Author(s):  
Sayed Saifullah ◽  
◽  
Amir Ali ◽  
Zareen A. Khan ◽  
Keyword(s):  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Gordon Equation ◽  
Numerical Solutions ◽  
Soliton Solutions ◽  
Double Laplace Transform ◽  
General Series ◽  
Klein Gordon ◽  
Localized Mode ◽  
Klein Gordon Equation

<abstract><p>We investigate the nonlinear Klein-Gordon equation with Caputo fractional derivative. The general series solution of the system is derived by using the composition of the double Laplace transform with the decomposition method. It is noted that the obtained solution converges to the exact solution of the model. The existence of the model in the presence of Caputo fractional derivative is performed. The validity and precision of the presented method are exhibited with particular examples with suitable subsidiary conditions, where good agreements are obtained. The error analysis and its corresponding surface plots are presented for each example. From the numerical solutions, we observe that the proposed system admits soliton solutions. It is noticed that the amplitude of the wave solution increases with deviations in time, that concludes the factor $ \omega $ considerably increases the amplitude and disrupts the dispersion/nonlinearity properties, as a result, may admit the excitation in the dynamical system. We have also depicted the physical behavior that states the advancement of localized mode excitations in the system.</p></abstract>

Solutions of the Coupled Klein-Gordon Equation by Modified Exp-Function Method

2011 ◽  
Vol 3 (3) ◽  
pp. 276-278
Author(s):  
Ram Dayal Pankaj ◽  
◽  
Arun Kumar
Keyword(s):  
Function Method ◽  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals Fractional Klein-Gordon equation with singular mass

2021 ◽  
Vol 143 ◽  
pp. 110579
Author(s):  
Arshyn Altybay ◽  
Michael Ruzhansky ◽  
Mohammed Elamine Sebih ◽  
Niyaz Tokmagambetov
Keyword(s):  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation
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