Stability for an Klein–Gordon equation type with a boundary dissipation of fractional derivative type

2021 ◽  
pp. 1-25
Author(s):  
Jaime Muñoz Rivera ◽  
Verónica Poblete ◽  
Octavio Vera
Keyword(s):  
Asymptotic Behavior ◽  
Fractional Derivative ◽  
Gordon Equation ◽  
Relativistic Equation ◽  
Derivative Type ◽  
Boundary Dissipation ◽  
Klein Gordon ◽  
Klein Gordon Equation

We consider an Klein–Gordon relativistic equation with a boundary dissipation of fractional derivative type. We study of stability of the system using semigroups theory and classical theorems over asymptotic behavior.

scholarly journals Conformable fractional derivative and its application to fractional Klein-Gordon equation

2019 ◽  
Vol 23 (6 Part B) ◽  
pp. 3745-3749
Author(s):  
Kangle Wang ◽  
Shaowen Yao
Keyword(s):  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Gordon Equation ◽  
Variational Iteration Method ◽  
Conformable Fractional Derivative ◽  
Fractional Complex Transform ◽  
Klein Gordon ◽  
Fractional Differential ◽  
Fractional Equation ◽  
Klein Gordon Equation

This paper adopts conformable fractional derivative to describe the fractional Klein-Gordon equations. The conformable fractional derivative is a new simple well-behaved definition. The fractional complex transform and variational iteration method are used to solve the fractional equation. The result shows that the proposed technology is very powerful and efficient for fractional differential equations.

scholarly journals DEVELOPMENT AND ANALYSIS OF NEW APPROXIMATION OF EXTENDED CUBIC B-SPLINE TO THE NONLINEAR TIME FRACTIONAL KLEIN–GORDON EQUATION

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040039 ◽  
Author(s):  
TAYYABA AKRAM ◽  
MUHAMMAD ABBAS ◽  
MUHAMMAD BILAL RIAZ ◽  
AHMAD IZANI ISMAIL ◽  
NORHASHIDAH MOHD. ALI
Keyword(s):  
Fractional Derivative ◽  
Numerical Solution ◽  
Gordon Equation ◽  
Basis Functions ◽  
Unconditionally Stable ◽  
B Spline ◽  
Numerical Examples ◽  
Caputo’S Fractional Derivative ◽  
Klein Gordon ◽  
Klein Gordon Equation

A new extended cubic B-spline (ECBS) approximation is formulated, analyzed and applied to obtain the numerical solution of the time fractional Klein–Gordon equation. The temporal fractional derivative is estimated using Caputo’s discretization and the space derivative is discretized by ECBS basis functions. A combination of Caputo’s fractional derivative and the new approximation of ECBS together with [Formula: see text]-weighted scheme is utilized to obtain the solution. The method is shown to be unconditionally stable and convergent. Numerical examples indicate that the obtained results compare well with other numerical results available in the literature.

scholarly journals The Initial Value Problem for the Quadratic Nonlinear Klein-Gordon Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-35 ◽  
Author(s):  
Nakao Hayashi ◽  
Pavel I. Naumkin
Keyword(s):  
Asymptotic Behavior ◽  
Initial Data ◽  
Compact Support ◽  
Initial Value Problem ◽  
Normal Forms ◽  
Gordon Equation ◽  
Initial Value ◽  
Klein Gordon ◽  
Klein Gordon Equation

We study the initial value problem for the quadratic nonlinear Klein-Gordon equation , , , , where and . Using the Shatah normal forms method, we obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data which was assumed in the previous works.

scholarly journals Novel Recursive Approximation for Fractional Nonlinear Equations within Caputo-Fabrizio Operator

2018 ◽  
Vol 22 ◽  
pp. 01008 ◽  
Author(s):  
Mehmet Yavuz
Keyword(s):  
Fractional Derivative ◽  
Exact Solutions ◽  
Solution Method ◽  
Gordon Equation ◽  
Nonlinear Partial Differential Equations ◽  
Rapid Convergence ◽  
Derivative Operator ◽  
Klein Gordon ◽  
Novel Method ◽  
Klein Gordon Equation

This study displays a novel method for solving time-fractional nonlinear partial differential equations. The suggested method namely Laplace homotopy method (LHM) is considered with Caputo-Fabrizio fractional derivative operator. In order to show the efficiency and accuracy of the mentioned method, we have applied it to time-fractional nonlinear Klein-Gordon equation. Comparisons between obtained solutions and the exact solutions have been made and the analysis shows that recommended solution method presents a rapid convergence to the exact solutions of the problems.

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